Springer, 2024. — 450 p. This book delves into the p-adic Simpson correspondence, its construction, and development. Offering fresh and innovative perspectives on this important topic in algebraic geometry, the text serves a dual purpose: it describes an important tool in p-adic Hodge theory, which has recently attracted significant interest, and also provides a comprehensive...
Springer, 2010. — 320 p. The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety. The degrees of freedom of a moving point on the variety is the dimension of the variety. A one-dimensional variety is a curve and a two-dimensional variety is a surface. A three-dimensional variety may be called asolid. Most...
Berlin: Walter. de Gruyter, 2004. — 570 p. This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998). It presents a wide-ranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special...
Berlin: de Gruyter, 2004. — 1150 p. This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998). It presents a wide-ranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis...
Springer, 1970. — 187 p. These notes grew out of a Columbia seminar on Grothendieck's tfourbaki talk on duality and his SGA talks on flat, etale, and smooth morphisms. They are intended as a second course in algebraic geometry and assume only a general familiarity with schemes including Serre's theorems on the cohomology of projective space.
Cambridge: Cambridge University Press, 2023. — 462 p. Preface Preview Defining Equivariant Cohomology Basic Properties Grassmannians and flag varieties Localization I Conics Localization II Toric Varieties Schubert Calculus on Grassmannians Flag Varieties and Schubert Polynomials Degeneracy Loci Infinite-Dimensional Flag Varieties Symplectic Flag Varieties Symplectic Schubert...
New York: Spriner, 2021. — 337 p. This volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took...
New York: Springer, 2012. - 326 p.
This textbook is a strong addition to existing introductory literature on algebraic geometry. The author’s treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is also an ideal text for showing students the connections between algebraic geometry,...
Cambridge: Cambridge University Press, 2023. — 451 p. Algebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds are a fundamental subclass that can be thought of as higher-dimensional generalizations of ordinary spheres. They belong to 105 irreducible deformation families. This book determines whether the general element of each family admits a...
Springer, 2017. — 294 p. This volume is an outcome of the International conference held in Tata Institute of Fundamental Research and University of Hyderabad. There are fifteen articles in this volume. The main purpose of the articles is to introduce recent and advanced techniques in the area of Analytic and Algebraic Geometry. This volume attempts to give recent developments in...
Cambridge: Cambridge University Press, 1998. — 445 p. Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists, and systems theorists, their study is now flourishing. This volume, an outgrowth of a 1995 program at the Mathematical Sciences Research...
Boston: Birkhäuser, 2003. — 218 p. This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology). In particular, it develops a novel algebraic tool in this field: rooted in the concept of critical...
Cambridge University Press, 2008. — 208 p. — (New Mathematical Monographs: 9). There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing...
Springer, 2022. — 395 p. — (Infosys Science Foundation Series in Mathematical Sciences). — ISBN 978-981-16-7120-3. This book contains selected chapters on perfectoid spaces, their introduction and applications, as invented by Peter Scholze in his Fields Medal winning work. These contributions are presented at the conference on “Perfectoid Spaces” held at the International...
Springer, 2022. — 603 p. — (Infosys Science Foundation Series in Mathematical Sciences). — ISBN 978-981-16-7121-0. This book contains selected chapters on perfectoid spaces, their introduction and applications, as invented by Peter Scholze in his Fields Medal winning work. These contributions are presented at the conference on “Perfectoid Spaces” held at the International...
Cambridge University Press. — 132 p. The classification of algebraic surfaces is an intricate and fascinating branch of mathematics, developed over more than a century and still an active area of research today. In this book, Professor Beauville gives a lucid and concise account of the subject, expressed simply in the language of modern topology and sheaf theory, and accessible...
Lecture notes. — Behrend Kai, 2012. — 127 p. These are lecture notes based on a short course on stacks given at the Newton Institute in Cambridge in January 2011. They form a self-contained introduction to some of the basic ideas of stack theory. Stacks and algebraic stacks were invented by the Grothendieck school of algebraic geometry in the 1960s. One purpose, was to give...
Cambridge: Cambridge University Press, 2016. — 360 p. — ISBN: 978-1-107-57003-0. There are many interactions between noncommutative algebra and representation theory on the one hand and classical algebraic geometry on the other, with important applications in both directions. The aim of this book is to provide a comprehensive introduction to some of the most significant topics...
Cambridge: Cambridge University Press, 2023. — 307 p. The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results,...
European Mathematical Society, 2009. — 507 p. — (EMS Textbooks in Mathematics) — ISBN: 9783037190647 This book consists of lectures on classical algebraic geometry, that is, the methods and results created by the great geometers of the late nineteenth and early twentieth centuries. This book is aimed at students of the last two years of an undergraduate program in mathematics:...
Berlin: Springer, 1997. — 139 p. This book provides a unified combinatorial realization of the categroies of (closed, oriented) 3-manifolds, combed 3-manifolds, framed 3-manifolds and spin 3-manifolds. In all four cases the objects of the realization are finite enhanced graphs, and only finitely many local moves have to be taken into account. These realizations are based on the...
American Mathematical Society, 2019. — 358 p. — (Contemporary mathematics). — ISBN: 9781470451530, 1470451530. This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography,...
Salerno: Springer-INdAM, 2023. — 371 p. An incredible season for algebraic geometry flourished in Italy between 1860, when Luigi Cremona was assigned the chair of Geometria Superiore in Bologna, and 1959, when Francesco Severi published the last volume of the treatise on algebraic systems over a surface and an algebraic variety. This century-long season has had a prominent...
2nd edition. — Springer Science & Business Media, 2013. — 638 p. This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture....
Basel: Birkhäuser, 2013. — 210 p. The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of Riemann–Roch–Grothendieck for proper submersions. It gives an equality of cohomology classes in Bott–Chern cohomology, which is a refinement for complex manifolds of de Rham cohomology. When the manifolds are Kähler, our main...
New York: Springer, 2006. — 355 p.
Conics and Cubics is an accessible introduction to algebraic curves. Its focus on curves of degree at most three keeps results tangible and proofs transparent. Theorems follow naturally from high school algebra and two key ideas, homogeneous coordinates and intersection multiplicities.
By classifying irreducible cubics over the real numbers...
Cham: Birkhäuser, 2024. — 252 p. This monograph deals with the Hadamard products of algebraic varieties. A typical subject of study in Algebraic Geometry are varieties constructed from other geometrical objects. The most well-known example is constituted by the secant varieties, which are obtained through the construction of the join of two algebraic varieties, which, in turn,...
Basel: Birkhäuser, 2014. — 337 p. This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses...
Springer International Publishing AG, 2017. — 267 p. — (Simons Symposia) — ISBN: 9783319497624 Geometry Over Nonclosed Fields is a reference to an active area at the interface of classical algebraic geometry and arithmetic geometry. In recent years, there has been a rapid exchange of ideas between these domains: many questions concerning integral or rational solutions of...
Springer International Publishing AG, 2017. — 267 p. — (Simons Symposia) — ISBN: 9783319497624. Geometry Over Nonclosed Fields is a reference to an active area at the interface of classical algebraic geometry and arithmetic geometry. In recent years, there has been a rapid exchange of ideas between these domains: many questions concerning integral or rational solutions of...
Cambridge University Press, 2007 — 670 pp. — (New Mathematical Monographs: 4). Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a rich area of ideas such as Fermat's Last Theorem, and most recently the ABC conjecture. This monograph is a bridge between the classical theory and modern approach...
2nd ed. — Springer, 2022. — 507 p. — (Universitext). — ISBN 1447175220. Algebraic Geometry is a fascinating branch of Mathematics that combines methods from both Algebra and Geometry. It transcends the limited scope of pure Algebra by means of geometric construction principles. Putting forward this idea, Grothendieck revolutionized Algebraic Geometry in the late 1950s by...
Birkhäuser, 2024. - 224 p. - (Oberwolfach Seminars, 53). - ISBN 3031514610. Metric algebraic geometry combines concepts from algebraic geometry and differential geometry . Building on classical foundations, it offers practical tools for the 21st century. Many applied problems center around metric questions, such as optimization with respect to distances . After a short dive...
Paris: European Mathematical Society, 2018. — 357 p. This volume is a collection of contributions by the participants of the conference IMPANGA15, organized by participants of the seminar, as well as notes from the major lecture series of the seminar in the period 2010–2015. Both original research papers and self-contained expository surveys can be found here. The articles...
Singapore: World Scientific Publishing. - 1998. -219 p. In 1989-1990 I taught a course in Algebraic Geometry at Stanford University, writing up lecture notes. These were revised for publication in 1998. In 1989-90 I covered the material in Chapters 1-14 in two quarters, and continued with a quarter on cohomology of coherent sheaves, lecturing out of Hartshorne’s book. The aim...
Springer, 2023. — 220 p. This volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to higher dimensional varieties) from different aspects: the historical development that led to the theory of algebraic surfaces...
Springer, 2011. — 631 p. — (Advances in Mathematics Education). — ISBN: 978-3-642-17734-7. In recent years there has been increased interest in the development of students’ algebraic thinking in the elementary and middle school grades. This important and timely new volume contains the most comprehensive collection of research focused on early algebraization. The volume’s...
New York: Springer, 2019. — 237 p. The book presents the central facts of the local, projective and intrinsic theories of complex algebraic plane curves, with complete proofs and starting from low-level prerequisites. It includes Puiseux series, branches, intersection multiplicity, Bézout theorem, rational functions, Riemann-Roch theorem and rational maps. It is aimed at...
Cambridge: Cambridge University Press, 2016. — 195 p. Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this...
Springer Science+Business Media, Singapore, and Hindustan Book, Agency, 2016. — 82 p. — (Institute of Mathematical Sciences-lecture Notes 3) — ISBN: 9380250835. This book is intended to be an introduction to Diophantine Geometry. The central theme is the investigation of the distribution of integral points on algebraic varieties. This text rapidly introduces problems in...
World Scientific, 2002. - 507 pp. This invaluable book contains the collected papers of Prof Wei-Liang Chow, an original and versatile mathematician of the 20th Century. Prof Chow's name has become a household word in mathematics because of the Chow ring, Chow coordinates, and Chow's theorem on analytic sets in projective spaces. The Chow ring has many advantages and is widely...
Springer, 2018. — 330 p. — (Abel Symposia). — ISBN: 978-3-319-94880-5. The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this...
Springer-Verlag, 1983. - 418 p. ISBN: 3540123202.
The Conference on "Open problems in Algebraic Geometry" was held in Ravello ( Salerno ) during the week: May 31 st- June 5 th, 1982 . This volume contains most of the lectures and talks given during the Conference as well as papers grown up from discussions among participants.
European Mathematical Society, 2020. — 145 p. — (EMS Series of Lectures in Mathematics 31). — ISBN-13 9783037192108. Τhe classification of complex algebraic surfaces is a very classical subject which goes back to the old Italian school of algebraic geometry with Enriques and Castelnuovo. However, the exposition in the present book is modern and follows Mori's approach to the...
Springer, 2021. — 326 p. — (UNITEXT - La Matematica per il 3+2, 129). — ISBN 978-3-030-71020-0. This book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective...
Springer, 2021. — 326 p. — (UNITEXT - La Matematica per il 3+2, 129). — ISBN 978-3-030-71020-0. This book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective...
Cambridge University Press, 2011. — x, 310 p. — (London Mathematical Society Lecture Note Series, 393). — ISBN 1-107-64885-8, 978-1-107-64885-2. Number theory currently has at least three different perspectives on non-abelian phenomena: the Langlands programme, non-commutative Iwasawa theory and anabelian geometry. In the second half of 2009, experts from each of these three...
Springer-Verlag, 2013. — xii, 206 p. — (Springer Proceedings in Mathematics & Statistics, 29). — ISBN 978-3-642-32198-6, 978-3-642-32199-3. The mysterious link between special values of complex zeta and L-functions and purely arithmetic problems was discovered by Dirichlet and Kummer in the nineteenth century, and spectacularly generalized in the twentieth century by Birch and...
Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo. — Springer-Verlag, 1999. — viii, 260 p. — (Lecture Notes in Mathematics, 1716). — ISBN 978-3-540-66546-5, 978-3-540-48160-7. This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997....
Springer, 2000. — 300 p. Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves,...
New York: Springer, 2020. — 186 p. — (Universitext). — ISBN: 978-3-030-43780-0, 978-3-030-43781-7. This English translation of Daniel Coray’s original French textbook Notes de géométrie et d’arithmétique introduces students to Diophantine geometry. It engages the reader with concrete and interesting problems using the language of classical geometry, setting aside all but the...
Springer, 1986. — 353 p. — ISBN10: 1461386578; ISBN13: 978-1461386575. This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these...
AMS, 2017. — 386 p. — (Proceedings of Symposia in Pure Mathematics 95). — ISBN 9781470435578. The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental...
Fourth Edition. — Springer, 2015. — 653 p. — ISBN: 978-3-319-16720-6. This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are...
Springer, 2006. — 551 p. — 2nd ed. — (Undergraduate Texts in Mathematics). — ISBN: 0387946802, 9780387946801
Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and...
Springer, 2006. — 344 p. — (Algorithms and Computation in Mathematics (AACIM) 16). Systems of polynomial equations are central to mathematics and its application to science and engineering. Their solution sets, called algebraic sets, are studied in algebraic geometry, a mathematical discipline of its own. Algebraic geometry has a rich history, being shaped by different schools....
Cambridge: Cambridge University Press, 2013. — 133 p. Most of mathematics is concerned at some level with setting up and solving various types of equations. Algebraic geometry is the mathematical discipline which handles solution sets of systems of polynomial equations. These are called algebraic sets. Making use of a correspondence which relates algebraic sets to ideals in...
De Gruyter, 2012. — 412 p. This monograph summarizes and extends a number of results on the topology of trigonal curves in geometrically ruled surfaces. An emphasis is given to various applications of the theory to a few related areas, most notably singular plane curves of small degree, elliptic surfaces, and Lefschetz fibrations (both complex and real), and Hurwitz equivalence...
Berlin: Springer-Verlag, 1981. — 422 p. Front Matter General Introduction Notations and Conventions Hodge Cycles on Abelian Varieties Tannakian Categories Langlands’s Construction of the Taniyama Group Motifs et Groupes de Taniyama Conjugates of Shimura Varieties Hodge Cycles and Crystalline Cohomology Addendum 1989 General Introduction Notations and Conventions Hodge Cycles on...
Cambridge, UK: Cambridge University Press 2015. — 538 p. — (London Mathematical Society Lecture Note 420). — ISBN: 1107462541. The 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern...
Basel: Birkhäuser, 2011. — 569 p. This generalization of geometry is bound to have wide spread repercussions for mathematics as well as physics. The unearthing of it will entail a new golden age in the interaction of mathematics and physics. E. Witten (1986) The idea that the moduli space Mg of curves of fixed genus 9 - that is, the algebraic variety that parametrizes all...
Cambridge University Press, 2012. — 652 p. — ISBN: 1107017653, 9781107017658. Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical...
Seoul National University, 1994. — 147 p. — (Lectures Notes, 25). These notes originate in a series of lectures given at the Tokyo Metropolitan University and Seoul National University in the Fall of 1993. These lectures have been extended into a graduate course at the University of Michigan in the Winter of 1994. Almost all of the material in these notes had been actually...
Б.м., б.и, 2003. — 232 p. The primary goal of this book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of...
Published online. — 2010 (Sept. 27). — 524 (x+514) p. English. Interactive menu. The main purpose of the present treatise is to give an account of some of the topics in algebraic geometry which while having occupied the minds of many mathematicians in previous generations have fallen out of fashion in modern times. Often in the history of mathematics new ideas and techniques...
Cambridge University Press, 2020. — 422 p. — (London Mathematical Society Lecture Note Series, 458). — ISBN: 978-1-108-71574-4. Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many...
Cambridge University Press, 2020. — 536 p. — (London Mathematical Society Lecture Note Series, 459). — ISBN: 978-1-108-71577-5. Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many...
New York: Springer, 2004. — 784 p. Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials,...
Springer, 2005. — 252 p. — ISBN: 0-387-22215-4. First textbook-level account of basic examples and techniques in this area. Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already.
Cambridge: Cambridge University Press, 2016. — 630 p. This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational...
Springer, 2000. — 310 p. — (Graduate Texts in Mathematics 197). — ISBN: 978-0-387-22639-2. "Both Eisenbud and Harris are experienced and compelling educators of modern mathematics. This book is strongly recommended to anyone who would like to know what schemes are all about." Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its...
Berlin: Springer-Verlag, 2002. — 334 p. Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re cently developed algorithms have made theoretical aspects of the subject accessible to a broad range of...
Springer, 2005. — 214 p. — (Springer Monographs in Mathematics). — ISBN: 354024221X, 3642063454. Absolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must...
CRC Press, 2017. — 258 p. — (Monographs And Research Notes In Mathematics) — ISBN: 149879601X. Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry. This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of...
Springer, 2023. — 96 p. The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is, its complex local systems. A fundamental problem is then to single out the complex points of such moduli spaces which correspond to geometric systems, and more...
Cambridge: Cambridge University Press, 2023. — 241 p. Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these...
Springer, 2018 (Reprint of the 1990 Edition). — 211 p. —— (Series: Modern Birkhäuser Classics). — ISBN: 978-3-319-98025-6. "An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical...
Birkhäuser, 2018. — x+390 p. — (Modern Birkhäuser Classics). — ISBN: 978-3-319-96574-1. "An introduction to the ideas of algebraic geometry in the motivated context of system theory." This describes this two volume work which has been specifically written to serve the needs of researchers and students of systems, control, and applied mathematics. Without sacrificing...
Basel: Birkhäuser, 2021. — 440 p. This book provides an overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces and birational invariants of group actions on...
CRC Press, 2019. — xxx, 226 p. — ISBN: 978-1-138-32257-8, 978-1-138-59051-9. True PDF "Pencils of Cubics and Algebraic Curves in the Real Projective Plane" thoroughly examines the combinatorial configurations of n generic points in RP². Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first...
World Scientific, 2023. — xx, 306 p. — (Essential Textbooks in Mathematics). — ISBN 978-1-80061-265-5, 978-1-80061-274-7, 978-1-80061-266-2, 978-1-80061-267-9. This book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract...
Cambridge: Cambridge University Press, 2024. — 218 p. Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional...
American Mathematical Society, 2001. — 356 p. Vertex algebras were first introduced as a tool used in the description of the algebraic structure of certain quantum field theories. It became increasingly important that vertex algebras are useful not only in the representation theory of infinite-dimensional Lie algebras, where they are by now ubiquitous, but also in other fields,...
American Mathematical Society, 2017. — 581 p. — (Mathematical Surveys and Monographs 217). — ISBN 9781470434816. The Grothendieck-Teichmuller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this book is to explain that this group has a topological interpretation as a group of...
American Mathematical Society, 2017. — 743 p. — (Mathematical Surveys and Monographs 217). — ISBN 9781470434816. The ultimate goal of this book is to explain that the Grothendieck-Teichmuller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this...
Princeton University Press, 2019. — x, 175 p. — (Annals of mathematics studies, 202). — ISBN: 978-0-691-19378-6, 978-0-691-19377-9. True PDF Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures - which were delivered in celebration of the tenth anniversary of the...
Addison-Wesley, 1969. — 234 p. Although algebraic geometry is a highly developed and thriving field of mathematics, it is notoriously difficult for the beginner to make his way into the subject. There are several texts on an undergraduate level that give an excellent treatment of the classical theory of plane curves, but these do not prepare the student adequately for modern...
Princeton University Press, 1993. — 157 p. Definitions and examples. Singularities and compactness. Orbits, topology, and line bundles. Moment maps and the tangent bundle. Intersection theory.
American Mathematical Society, 2017. — 533 p. — (Mathematical Surveys and Monographs). — ISBN: Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic...
American Mathematical Society, 2017. — 474 p. — (Mathematical Surveys and Monographs 221). — ISBN: 1470435705. Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in other parts of mathematics, most prominently in representation theory. This volume develops deformation theory, Lie theory and the theory of...
Hoboken: Wiley, 1987. — 328 p. Offers a unified treatment of both the modern and the classical aspects of Teichmuller theory. The classical parts of the theory include Teichmuller's theorem on the existence and uniqueness of an extremal quasiconformal mapping in a given homotopy class of mappings between Riemann surfaces, the theorems of Bers and Ahlfors on the completeness of...
Park City Mathematics Institute (PCMI), 2015. — 41 p. Twelve lectures were given by Undergraduate Summer School. These lectures were noted by David Mehrle.
Oxford: Oxford University Press, 2013. — 319 p. — ISBN: 019967616X. An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level , this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material...
American Mathematical Society, 2003. — 366 p. Algebraic geometry and geometric modeling both deal with curves and surfaces generated by polynomial equations. Algebraic geometry investigates the theoretical properties of polynomial curves and surfaces; geometric modeling uses polynomial, piecewise polynomial, and rational curves and surfaces to build computer models of...
New York: Springer, 1989. - 297p.
A recent paper on subfactors of von Neumann factors has stimulated much research in von Neumann algebras. It was discovered soon after the appearance of this paper that certain algebras which are used there for the analysis of subfactors could also be used to define a new polynomial invariant for links. Recent efforts to understand the...
Unpublished. — Moscow, Fall 2017. — 125 p. This is a geometric introduction to the algebraic geometry. I hope to acquaint the readers with some basic figures underlying the modern algebraic technique and show how to translate things from the infinitely rich (but quite intuitive) world of figures to the scanty and finite (but very explicit) language of formulas. These lecture...
2nd Edition. — Springer, 2020. — 634 p. — (Springer Studium Mathematik – Master). — ISBN: 978-3-658-30732-5. This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the...
Wiesbaden: Springer Spektrum, 2023. — vIII, 870 p. — (Springer Studium Mathematik - Master). — ISBN 978-3-658-43030-6, 978-3-658-43031-3. This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and étale...
Springer, 2010. — 622 p. — ISBN: 978-3-8348-0676-5. This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to...
Princeton University Press, 2012. — 297 p. Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource...
Springer, 2018. — 604 p. — ISBN: 978-3-319-96826-1. This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and...
State University of New York at Buffalo, 2016. — 166 p. Algebraic geometry is the place where the algebra involved in solving systems of simultaneous multivariable polynomial equations meets the geometry of curves, surfaces, and higher dimensional algebraic varieties. In algebraic geometry, a functor represented by a scheme X is a set-valued contravariant functor on the...
Paris: Société Mathématique de France, 2023. — 288 p. The aim of this paper is to apply the microlocal theory of sheaves of Kashiwara-Schapira to the symplectic geometry of cotangent bundles, following ideas of Nadler-Zaslow and Tamarkin. We recall the main notions and results of the microlocal theory of sheaves, in particular the microsupport of sheaves. The microsupport of a...
Cambridge: Cambridge University Press,2015. — 451 p. Contemporary research in algebraic geometry is the focus of this collection, which presents articles on modern aspects of the subject. The list of topics covered is a roll-call of some of the most important and active themes in this thriving area of mathematics: the reader will find articles on birational geometry, vanishing...
Springer International Publishing, 2016. — 151 p. — (Lecture Notes in Mathematics 2156). — ISBN: 978-3-319-26638-1; 978-3-319-26637-4. Presenting the first systematic treatment of the behavior of Néron models under ramified base change, this book can be read as an introduction to various subtle invariants and constructions related to Néron models of semi-abelian varieties,...
Cambridge: Cambridge University Press, 2023. — 201 p. This clear and elegant text introduces Künneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic development of the foundations of Lagrangian foliations. The...
Amer Mathematical Society, 2017. — 216 p. — (Memoirs of the American Mathematical Society). — ISBN10: 147042312X, ISBN13: 978-1470423124. We give two simple generalizations of commutative rings. They form (co)-complete categories, that contain commutative (semi-) rings (e.g. with the usual multiplication ). But they also contains the "integers" (and ), and the "residue fields"...
World Scientific, 2004. — 117 p. This subject has been of great interest both to topologists and to number theorists. The first part of this book describes some of the work of Kuo-Tsai Chen on iterated integrals and the fundamental group of a manifold. The author attempts to make his exposition accessible to beginning graduate students. He then proceeds to apply Chen’s...
Springer, 1977. — 511 p. — (Graduate Texts in Mathematics 52). — ISBN: 978-1-4419-2807-8. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he...
Cambridge University Press, 2007. - 266 pages. Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as...
Andreas Hermann, 2005. — 228 p. Algebraic Geometry is an ancient discipline of mathematics that has undergone several revolutions throughout its history. Nowadays one should distinguish between two different kinds of algebraic geometry: elementary and scheme-theoretic algebraic geometry. The elementary theory studies geometric objects defined by polynomial equations by...
New York: Springer, 2000. — 570 p. This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Princeton University Press, 2008. — 718 p. — (Princeton Series in Applied Mathematics). — ISBN: 978-0-691-09679-7. This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite...
Cambridge University Press, 1994. — 444 p. — (Cambridge Mathematical Library). — ISBN: 0521469007, 9780521469005
This classic work (first published in 1947), in three volumes, provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed...
Cambridge University Press, 1994. — 402 p. — (Cambridge Mathematical Library). — ISBN: 0521469015, 9780521469012, 0521469074, 0521467756
Volume 2 gives an account of the principal methods used in developing a theory of algebraic varieties on n dimensions, and supplies applications of these methods to some of the more important varieties that occur in projective geometry.
Cambridge University Press, 1994. — 342 p. — (Cambridge Mathematical Library). — ISBN: 0521467756, 9780521467759, 0521469074, 0521469015
In the third volume, the authors discuss algebraic varieties on a ground field without characteristic, and deal with more advanced geometrical methods, such as valuation theory.
Springer, 2012. — 365 p. — ISBN: 978-3-642-19224-1. This book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to read all of his work Elements. Euclid is said to have answered: “There is no royal road to geometry!”...
Basel: Birkhäuser, 1994. — 167 p. Elliptic Curves, the Finiteness Theorem of Shafarevič Elliptic Curves over ℂ Elliptic Curves over Arbitrary Fields Picard Curves The Moduli Space of PICARD Curves The Relative SCHOTTKY Problem for PICARD Curves Typical Period Matrices Metrization Arithmetization A Retrospect to Elliptic Curves Rough Solution of the Relative SCHOTTKY Problem for...
Princeton: Princeton University Press, 2016. — 226 p. Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural...
Berlin: ds Gruyter, 1993. — 360 p. Introduction Compactified moduli spaces Moduli spaces Torus embeddings and applications Toroidal compactification of A(1, p) The boundary of A*(1, p) Humbert surfaces and scaffoldings The Satake compactification Degenerations of abelian surfaces Mumford’s construction The basic construction for surfaces Degenerate abelian surfaces (the...
American Mathematical Society, 2000. — 213 p. Introduction. Affine Varieties. Projective Varieties. Smooth Points and Dimension. Plane Cubic Curves. Cubic Surfaces. Introduction to the Theory of Curves.
2nd Edition. — Braunschweig; Wiesbaden: Vieweg, 1992. — viii, 240 p. — (Aspects of mathematics: E; Vol. 18). — ISBN 978-3-528-06433-4, 978-3-322-85466-7. In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last...
Springer, 2021. — 27965 p. — (Springer Monographs in Mathematics). — ISBN 978-3-030-69804-1. What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations...
New York: Springer, 2021. — 637 p. What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from...
Clarendon Press, 2006. — 315 p. This seminal text on Fourier-Mukai Transforms in Algebraic Geometry by a leading researcher and expositor is based on a course given at the Institut de Mathematiques de Jussieu in 2004 and 2005. Aimed at postgraduate students with a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a...
Cambridge University Press, 2016. — 498 p. — (Cambridge studies in advanced mathematics 158). — ISBN13: 9781316594193. K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi-Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs,...
2nd ed. — Cambridge: Cambridge University Press, 2010. — 345 p. Now back in print, this highly regarded book has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces, which include moduli spaces in positive characteristic, moduli spaces of principal bundles and of complexes, Hilbert schemes of points on surfaces, derived...
Springer, 1982. — 365 p. The aim of this book is to introduce the reader to the geometric theory of algebraic varieties, in particular to the birational geometry of algebraic varieties. This volume grew out of the author's book in Japanese published in 3 volumes by Iwanami, Tokyo, in 1977. While writing this English version, the author has tried to rearrange and rewrite the...
2nd Edition. — American Mathematical Society, 2002. — 234 p. — (Graduate Studies in Mathematics 53). — ISBN 13 9780821831601. Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic...
Springer, 2014. — xxvi, 872 p. — (Springer Collected Works in Mathematics). — ISBN 4-431-55055-0, 978-4-431-55055-6. Kenkichi Iwasawa was one of the most original and influential mathematicians of the twentieth century. He made a number of fundamental contributions in group theory and algebraic number theory. In group theory, he created the theory of (L)-groups (including the...
Cambridge: Cambridge University Press, 2016. — 236 p. Originally published in 1916, this book was written to provide readers with a concise account of the leading properties of quartic surfaces possessing nodes or nodal curves. A brief summary of the leading results discussed in the book is included in the form of an introduction. This book will be of value to anyone with an...
Cambridge: Cambridge University Press, 2023. — 503 p. The first book on the explicit birational geometry of complex algebraic threefolds arising from the minimal model program, this text is sure to become an essential reference in the field of birational geometry. Threefolds remain the interface between low and high-dimensional settings and a good understanding of them is...
Cambridge: Cambridge University Press, 2024. — 262 p. The finite generation theorem is a major achievement in modern algebraic geometry. Based on the minimal model theory, it states that the canonical ring of an algebraic variety defined over a field of characteristic 0 is a finitely generated graded ring. This graduate-level text is the first to explain this proof. It covers...
Springer Nature Switzerland AG, 2018. — xiv+ 231 p. — (Moscow lectures, vol. 2). — ISBN: 978-3-030-02943-2. This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The...
American Mathematical Society, 2021. — 226 p. — (AMS/MAA Dolciani Mathematical Expositions, 57). — ISBN 978-1470456221. Challenge: Can you find all the integers a, b, c satisfying 2a2+3b2=5c2? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! There are infinitely many possibilities, and as any computer will...
Springer, 1977. — 316 p. — ISBN: 0-387-90199-X. This book was written to make learning introductory algebraic geometry as easy as possible. It is designed for the general first- and second-year graduate student, as well as for the nonspecialist; the only prerequisites are a one-year course in algebra and a little complex analysis. There are many examples and pictures in the...
Cambridge: Cambridge University Press, 1992. — 271 p. Complex algebraic curves were developed in the nineteenth century. They have many fascinating properties and crop up in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired by most undergraduate courses in mathematics, Dr...
Springer, 2020. — 86 p. — ISBN: 9811573794. This is an English translation of the book in Japanese, published as the volume 20 in the series of Seminar Notes from The University of Tokyo that grew out of a course of lectures by Professor Kunihiko Kodaira in 1967. It serves as an almost self-contained introduction to the theory of complex algebraic surfaces, including concise...
Princeton University Press, 2023. — 240 p. A pioneering new nonlinear approach to a fundamental question in algebraic geometry One of the crowning achievements of nineteenth-century mathematics was the proof that the geometry of lines in space uniquely determines the Cartesian coordinates, up to a linear ambiguity. What Determines an Algebraic Variety? develops a nonlinear...
European Mathematical Society, 2020. — 252 p. — (Tracts in Mathematics 32). — ISBN: 978-3-03719-208-5. Surfaces are a key piece in the classification of complex analytic or algebraic surfaces. The term was coined by A. Weil in 1958 – a result of the initials Kummer, Kähler, Kodaira, and the mountain K2 found in Karakoram. The most famous example is the Kummer surface discovered...
Springer, 2024. — 167 p. This book develops a C*-algebraic approach to the notion of principal symbol on Heisenberg groups and, using the fact that contact manifolds are locally modeled by Heisenberg groups, on compact contact manifolds. Applying abstract theorems due to Lord, Sukochev, Zanin, and McDonald, a principal symbol in the Heisenberg group is introduced as a...
Birkhäuser, 2021. — 480 p. — ISBN 3030626431. The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas...
Basel: Birkhäuser, 2005. — 288 p. This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed. Kunz's proven conception of teaching topics in commutative algebra together with their...
Berlin: Springer, 2006. — 412 p. — (Springer Monographs in Mathematics). — ISBN 3-540-23317-2, 978-3-540-23317-6. Serre's modularity conjecture, introduced by Jean-Pierre Serre (1975, 1987), states that an odd, irreducible, two-dimensional Galois representation over a finite field arises from a modular form. A stronger version of this conjecture specifies the weight and level...
Springer, 1983. — 383 p. — ISBN 978-1-4419-2818-4. Diophantine Geometry has been out of print for a while. Advances in algebraic geometry, especially in some ofthe problems ofdiophantine geometry, have motivated me to bring out a new book, and I thank Springer-Verlag for publishing it. Three years after Diophantine Geometry appeared, Neron published his fundamental paper giving...
2nd Edition. — Springer-Verlag, 1982. — x, 170 p. — (Graduate Texts in Mathematics, 89). — ISBN 978-1-4612-5742-4, 978-1-4612-5740-0. Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the...
New York: Springer, 2011. — 178 p. Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout the text. This volume is geared toward a second-year graduate...
Addison-Wesley 1973. 264 p. Algebraic geometry is the study of systems of algebraic equations in several variables, and:"of the structure which:" .one can give to the solutions of such equations There are four ways in which this study can b.e. carried out: ".analytic, topological, :'algebraico- geometric, and arithmetic. .:1 t :"aImost goes without...saying that. these four...
Springer Publications. 1983. 256 pages. Contents. Algebraic Groups. General Theorems on Abelian Varieties. The Theorem of the Square. Divisor Classes on an Abelian Variety. Functorial Formulas. The Picard Variety of an Arbitrary Variety. The l-Adic Representations. Algebraic Systems of Algebraic Varieties. Compositions of Correspondences.
Springer, 2023. — 390 p. — (Grundlehren Text Editions). — ISBN 978-3-031-25569-4. This textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles. The book begins...
Springer, 2003. — 372 p. — (A Series of Modern Surveys in Mathematics. Volume 48) — ISBN: 3540225285 This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the...
Springer, 2003. — 371 p. — (A Series of Modern Surveys in Mathematics. Volume 49) — ISBN: 9783540225348 This two-volume book on "Positivity in Algebraic Geometry" contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety,...
Berlin: Springer, 2004. — 244 p. This volume deals with various topics around equivariant holomorphic maps of Hermitian symmetric domains and is intended for specialists in number theory and algebraic geometry. In particular, it contains a comprehensive exposition of mixed automorphic forms that has never yet appeared in book form. The main goal is to explore connections among...
Boca Raton: CRC Press, 2000. — 393 p. Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory,...
World Scientific Publishing Co. Pte. Ltd., 2006. — ix+400 p. — (Series on number theory and its applications, 1). — ISBN: 981-256-814-X. Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations. More precisely, the goal is to bring...
Oxford University Press, 2006. — 594 p. This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more...
Springer, 2016. — xviii, 386 p. — (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Vol. 61). — ISBN 3-319-27369-8, 978-3-319-273698-3, 978-3-319-27371-6. This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of...
Springer, 2016. — 386 p. — (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Vol. 61). — ISBN: 3-319-27369-8, 978-3-319-27369-3, 978-3-319-27371-6. This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian...
New York: Springer, 2018. — 217 p. This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely circulated among Russian mathematicians. This book will be of...
World Scientific Publishing Co Pte Ltd, 2014. — 334 p. Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again...
World Scientific Publishing Co Pte Ltd, 2014 - 351 p. The present volume grew out of an international conference on affine algebraic geometry held in Osaka, Japan during 3-6 March 2011 and is dedicated to Professor Masayoshi Miyanishi on the occasion of his 70th birthday. It contains 16 refereed articles in the areas of affine algebraic geometry, commutative algebra and related...
The Mathematical Society of Japan, 1964. — 158 p. — (Publications of The Mathematical Society of Japan). Theoretical math written while the author was studying at The Institute for Advance Study, Princeton as a Guggenheim Fellow.
Providence: American Mathematical Society, 2010. — 601 p. Analytic and algebraic geometers often study the same geometric structures but bring different methods to bear on them. While this dual approach has been spectacularly successful at solving problems, the language differences between algebra and analysis also represent a difficulty for students and researchers in geometry,...
World Scientific Publishing Europe Ltd., 2021. — 615 p. — ISBN9781800610453. The development of inexpensive and fast computers, coupled with the discovery of efficient algorithms for dealing with polynomial equations, has enabled exciting new applications of algebraic geometry and commutative algebra. Algebraic Geometry for Robotics and Control Theory shows how tools borrowed...
World Scientific Publishing Europe Ltd., 2021. — 615 p. — ISBN9781800610453. The development of inexpensive and fast computers, coupled with the discovery of efficient algorithms for dealing with polynomial equations, has enabled exciting new applications of algebraic geometry and commutative algebra. Algebraic Geometry for Robotics and Control Theory shows how tools borrowed...
Independently published, 2023. - 223 p. These notes are an introduction to the theory of algebraic varieties emphasizing the similarities to the theory of manifolds . In contrast to most such accounts they study abstract algebraic varieties, and not just subvarieties of affine and projective space. This approach leads more naturally into scheme theory. Before learning scheme...
Publisher: J.S. Milne, 1998. - 157 pages.
These notes are an introduction to the theory of algebraic varieties. In contrast to most such accounts they study abstract algebraic varieties, and not just subvarieties of affine and projective space. This approach leads more naturally into scheme theory.
Singapore: World Scientific Publishing, 2020. — 456 p. Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where analyses will lead to further developments. In the present book, we...
World Scientific Publishing, 2024. — 440 p. — ISBN-13: 978-9811280085. Algebraic geometry is more advanced with the completeness condition for projective or complete varieties. Many geometric properties are well described by the finiteness or the vanishing of sheaf cohomologies on such varieties. For non-complete varieties like affine algebraic varieties, sheaf cohomology does...
Basel: Birkhäuser, 1991. — 258 p. The symposium "MEGA-90 - Effective Methods in Algebraic Geome try" was held in Castiglioncello (Livorno, Italy) in April 17-211990. The themes - we quote from the "Call for papers" - were the fol lowing: - Effective methods and complexity issues in commutative algebra, pro jective geometry, real geometry, algebraic number theory - Algebraic...
Hossein Movasati, 2020. — 380 p. What is Hodge Theory? The main purposes of the present book Prerequisites and how to read the book? Synopsis of the contents of this book Further reading Origins of Hodge theory Origins of singular homology Origins of de Rham cohomology The Legendre relation: a first manifestation of algebraic cycles Multiple integrals Tame polynomials and Hodge...
New York: Springer, 1999. — 76 p. This rare and an excellent book was published as an appendix to the second edition of the Mumford's "Red Book on Varieties and Schemes". Curves and Their Jacobians What is a Curve and How Explicitly Can We Describe Them? The Moduli Space of Curves: Definition, Coordinatization, and Some Properties How Jacobians and Theta Functions Arise The...
Berlin: Springer-Verlag, 1999. — 312 p. Mumford's famous Red Book gives a simple readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduate students or mathematicians in other fields wishing to learn quickly what algebraic geometry is all...
3rd ed. — Springer, 1994. — 294 p. — (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge). — ISBN10: 3642634001; ISBN13: 978-3642634000. "Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This...
Hindustan Book Agency (India), 2015. — 258 p. — (Texts and Readings in Mathematics 73) — ISBN10: 9380250800. Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book" containing notes of his lectures at Harvard University. Their genesis and evolution are described in the preface as: Initially notes to the course were...
Cambridge: Cambridge University Press, 2007. — 432 p. Manifolds Schemes The complex topology The analytification of a scheme The high road to analytification Coherent sheaves Projective space: the statements Projective space: the proofs The proof of GAGA Appendix 1. The proofs concerning analytification
Springer, 2022. — 732 p. This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology. In this way, it unites the analytic approach with the more recent topological one, combining their tools and methods. In the first chapters, the book sets out the foundations of...
Cham: Springer, 2023. — 456 p. The theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and...
Basel: Birkhäuser, 2023. — 167 p. This textbook provides a thorough introduction to spectrahedra, which are the solution sets to linear matrix inequalities, emerging in convex and polynomial optimization, analysis, combinatorics, and algebraic geometry. Including a wealth of examples and exercises, this textbook guides the reader in helping to determine the convex sets that can...
New Delhi: Tata Institute of Fundamental Research, 2012. — 163 p. Geometric Invariant Theory (GIT), developed in the 1960s by David Mumford, is the theory of quotients by group actions in algebraic geometry. The theory's principal application is to the construction of various moduli spaces. Newstead gave a series of lectures in 1975 at the Tata Institute of Fundamental...
Springer International Publishing AG, 2018. — ix+256 p. — (Lecture Notes in Mathematics, 2210). — ISBN: 978-3-319-75565-6. This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. Aimed at researchers and graduate students with an advanced background in algebra, these lectures were given during the Commutative...
London: World Scientific, 2020. — 311 p. This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they relate to the nature of the singularities on the variety. Since...
Berlin: Walter de Gruyter GmbH, 2017. — 276 p. This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is...
Cambridge University Press, 2018. — 559 p. — ISBN: 978-1-107-18773-3 This graduate textbook offers a self-contained introduction to the concepts and techniques of logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry and number theory. It features a systematic exposition of the foundations of the field, from the basic results on...
International Press of Boston, 2019. — 345 p. This book originated in the idea that open problems act as crystallization points in mathematical research. Mathematical books usually deal with fully developed theories. But here we present work at an earlier stage when challenging questions can give new directions to mathematical research. In mathematics, significant progress is...
Berlin: de Gruyter, 1994. — 348 p. The International Conference on "Zero-Dimensional Schemes" was held in Ravello (Salerno) from June 8 to 13, 1992. This volume contains most of the lectures given at the Conference as well as papers grown up from discussions among participants. In addition we have inserted at the end of the volume a list of problems and questions; most of them...
Springer, 1998. — 253 p. This EMS volume provides an exposition of the structure theory of Fano varieties, i.e. algebraic varieties with an ample anticanonical divisor. This book will be very useful as a reference and research guide for researchers and graduate students in algebraic geometry.
Springer, 2008. — 276 p. — ISBN: 1848000553
Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial...
Cambridge University Press, 2009. — 121 p. — (Cambridge Studies in Advanced Mathematics 47). — ISBN 13 9780521108478. Peskine doesn't give a lot of explanations (he manages to cover on 30 pages what usually takes up half a book) and the exercises are tough, but the book is nevertheless well written, which makes it pretty easy to read and understand. Recommended for everyone...
Springer, 2021. — 473 p. — (Lecture Notes in Mathematics 2276). — ISBN 978-3-030-57558-8.\ Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry...
Paris: EMS, 2022. — 182 p. Homological background A_∞- and A_n-structures Homological perturbation Relation of A_∞-structures to Hochschild cohomology Massey products for A_∞-categories and twisted objects Triangulated structure and generators Cyclic A_∞-structures G-invariant A_∞-structures Moduli spaces of A_∞-structures The moduli problem Nice quotients Representability...
Cambridge University Press, 2002. — 291 p. This book is a modern treatment of the theory of theta functions in the context of algebraic geometry. The novelty of its approach lies in the systematic use of the Fourier-Mukai transform. Alexander Polishchuk starts by discussing the classical theory of theta functions from the viewpoint of the representation theory of the Heisenberg...
Springer, 1998. — viii, 196 p. — (Lecture Notes in Mathematics, 1677). — ISBN 3-540-63751-6. The book is an introduction to the theory of cubic metaplectic forms on the 3-dimensional hyperbolic space and the author's research on cubic metaplectic forms on special linear and symplectic groups of rank 2. The topics include: Kubota and Bass-Milnor-Serre homomorphisms, cubic...
Cambridge University Press, 2020. — 331 p. — (London Mathematical Society Student Texts 97). — ISBN: 978-1-108-79044-4. Noncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988-92,...
De Gruyter, 2014. — 240 p. — ISBN: 3110316226, 9783110316223 Algebraic geometry has a complicated, difficult language. This book contains a definition, several references and the statements of the main theorems (without proofs) for every of the most common words in this subject. Some terms of related subjects are included. It helps beginners that know some, but not all, basic...
IMPA, 2003. — 124 p. This book is an introduction to the use and study of secant and tangent varieties to projective algebraic varieties. As mentioned in the Preface, these notes could also be thought of as a natural preparation to parts of the work of F. L. Zak [Tangents and secants of algebraic varieties}, Translated from the Russian manuscript by the author, Amer. Math....
Cham: Springer, 2021. — 172 p. This concise textbook gathers together key concepts and modern results on the theory of holomorphic foliations with singularities, offering a compelling vision on how the notion of foliation, usually linked to real functions and manifolds, can have an important role in the holomorphic world, as shown by modern results from mathematicians as H....
Paris: European Mathematical Society, 2008. — 397 p. The book starts with an introduction to Geometric Invariant Theory (GIT). The fundamental results of Hilbert and Mumford are exposed as well as more recent topics such as the instability flag, the finiteness of the number of quotients, and the variation of quotients. In the second part, GIT is applied to solve the classification...
Cambridge: Cambridge University Press, 1997. — 360 p. This book surveys progress in the domains described in the hitherto unpublished manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck. It will be of wide interest among workers in algebraic geometry, number theory, algebra and topology. Abstracts of the talks Dessins d'enfants Unicellular...
Cambridge: Cambridge University Press, 1997. — 302 p. The first of two volumes on anabelian algebraic geometry, this book contains the famous manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck. This work, written fourteen years after his retirement from public life in mathematics, includes the closely related letter to Gerd Faltings, published for...
Springer Spektrum, 2015. — 147 p. — ISBN: 978-3-658-11407-7. Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable Separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric...
University of Cambridge, 2017. — 97. Introduction Some preliminary analysis Characters of abelian groups Fourier transforms Mellin transform and Gamma-function Riemann zeta-function Dirichlet L-functions The modular group Modular forms of level 1 Basic definitions The space of modular forms Arithmetic of Delta Hecke operators Hecke operators and algebras Hecke operators on...
Cambridge: Cambridge University Press, 1999. — 503 p. This book is a conference proceedings based on the 1996 Durham Symposium on "Galois representations in arithmetic algebraic geometry". The title was interpreted loosely and the symposium covered recent developments on the interface between algebraic number theory and arithmetic algebraic geometry. The book reflects this and...
Springer, 2019. — xvi, 431 p. — (Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge / A Series of Modern Surveys in Mathematics, 70). — ISBN: 978-981-329-300-7, 978-981-32-9301-4. True PDF This book lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful...
Oxford: Clarendon Press, 1949. — 446 p. Классическая книга, которую можно рассматривать как развитие и продолжение более элементарного курса Semple and Kneebone, Algebraic projective geometry (хотя они и были написаны в обратном порядке). Plane curves The quadratic transformation Rational correspondences Systems of plane curves Linear systems of curves and their projective...
New York: A K Peters/CRC Press, 1997. — 203 p. This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat`s Last Theorem. The initial chapters are devoted to the Abelian case (complex...
Paris: Société Mathématique de France, 2020. — 199 p. As with many of the wonderful books that Serre has written, this one started with the notes of a series of lectures that Serre gave, this time during the Fall Semester of 1985 at Harvard University. The handwritten notes taken by F. Q. Gouvêa in 1985 circulated in photocopies or scanned PDF files, frequently cited as the...
De Gruyter, 2022. — 465 p. — (Expositions in Mathematics 70). — ISBN-13 9783110637540. The objective of this book is to look at certain commutative graded algebras that appear frequently in algebraic geometry. By studying classical constructions from geometry from the point of view of modern commutative algebra, this carefully-written book is a valuable source of information,...
World Scientific Publishing Europe, 2023. — 420 p. — ISBN 9781800613546. The book gives explicit computational methods and includes the most necessary prerequisites for understanding associative algebraic geometry. It focuses on the meaning and the place of deformation theory, resulting in a complete theory applicable to moduli theory. It answers the question "why moduli...
Cambridge University Press, 1992. — x, 186 p. — (Cambridge Studies in Advanced Mathematics, 33). — ISBN 0-521-41669-8, 978-0-521-41669-6. Arakelov theory is a new geometric approach to diophantine equations. It combines algebraic geometry in the sense of Grothendieck with refined analytic tools such as currents on complex manifolds and the spectrum of Laplace operators. It has...
Cambridge University Press, 1992. — x, 186 p. — (Cambridge Studies in Advanced Mathematics, 33). — ISBN 0-521-41669-8, 978-0-521-41669-6. Arakelov theory is a new geometric approach to diophantine equations. It combines algebraic geometry in the sense of Grothendieck with refined analytic tools such as currents on complex manifolds and the spectrum of Laplace operators. It has...
Springer, 2008. — 362 p. This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic...
Springer, 2008. — 180 p. — (The IMA Volumes in Mathematics and its Applications 148). — ISBN: 978-0-387-78132-7. Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over...
World Scientific Publishing Company, 2024. — 609 p. Complex Analytic Geometry is a subject that could be termed, in short, as the study of the sets of common zeros of complex analytic functions. It has a long history and is closely related to many other fields of Mathematics and Sciences, where numerous applications have been found, including a recent one in the Sato...
Pitman Publishing, 1977. — 127 p. The aim of this book Is to explain the development of the statements and proofs of the Well conjectures from the analogous results for the Riemann zeta function, at the same time describing the transformation of classical algebraic number theory and algebraic geometry into the language of schemes. In order to motivate the cohomological aspects...
Выходные данные и автор неизвестны. [Published online. — 2003 (June 5). — 185 (vi+179) p. English]. Polarity. Polar hypersurfaces: The polar pairing. First polars. Second polars. The Hessian. Parabolic points. The Steinerian. Dual hypersurface: The polar map. Dual varieties. Pl¨ucker equations. Exercises. Conics. Polar triangles: Conjugate triangles. Poncelet related conics....
Ravi Vakil, 2013. — 760 p. Early (out-of-date) version of "The Rising Sea: Foundations of Algebraic Geometry". Preliminaries Schemes Morphisms “Geometric” properties: Dimension and smoothness Quasicoherent sheaves More Bibliography Index
Stanford University, 2017. — 807 p. This book is intended to give a serious and reasonably complete introduction to algebraic geometry, not just for (future) experts in the field. The exposition serves a narrow set of goals, and necessarily takes a particular point of view on the subject. The reader should be familiar with some basic notions in commutative ring theory, in...
Marcel Dekker, 2000. — 296 p. This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theory...
Cambridge: Cambridge University Press, 2003. — 167 p. This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In...
Cambridge: Cambridge University Press, 2003. — 181 p. The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly, Nori's connectivity theorem, which generalizes the...
Cambridge University Press, 2002. — 335 p. — (Cambridge Studies in Advanced Mathematics 76). — ISBN13: 978-0-511-06352-7. This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in...
Cambridge University Press, 2003. — 363 p. — (Cambridge Studies in Advanced Mathematics 77). — ISBN13: 978-0-511-06355-8. The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and...
Société Mathématique de France, 2022. — x, 300 p. — (Astérisque, 432). — ISBN 978-2-85629-956-2, This manuscript presents a detailed and original account of the theory of opers defi ned on pointed stable curves in arbitrary characteristic and their moduli. In particular, it includes the development of the study of dormant opers, which are opers of a certain sort in positive...
Providence: American Mathematical Society, 2000. — 66 p. Reprinted with corrections, 2012. When information is transmitted, errors are likely to occur. This problem has become increasingly important as tremendous amounts of information are transferred electronically every day. Coding theory examines efficient ways of packaging data so that these errors can be detected, or even...
New York: Springer, 1978. — 208 p. This book was written to furnish a starting point for the study of algebraic geometry. The topics presented and methods of presenting them were chosen with the following ideas in mind; to keep the treatment as elementary as possible, to introduce some of the recently developed algebraic methods of handling problems of algebraic geometry, to...
Wiesbaden: Springer, 2016. — 366 p. This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of...
Société Mathématique de France, 2019. — vi, 140 p. — (Memoires de la Société Mathématique de France, 163). — ISBN 978-2-85629-909-8. Let W be the ring of the Witt vectors of a perfect field of characteristic p , χ a smooth formal scheme over W , χ' the base change of χ by the Frobenius morphism of W , χ' 2 the reduction modulo p ² of χ' and X the special fiber of χ. We lift the...
Singapore: World Scientific Publishing Company, 2021. — 282 p. — ISBN 9811238243. This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra...
Princeton University Press, 2012. — 174 p. This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension. The book is an...
Москва: Московский центр непрерывного математического образования (МЦНМО), 2009. — 88 с. — ISBN 9785940574439. Эта брошюра, написанная выдающимся современным математиком академиком РАН В.И. Арнольдом, основана на прочитанных автором популярных лекциях для старшеклассников. В живой и увлекательной форме излагаются основы теории алгебраических кривых в самых разных аспектах: от...
Монография. — Пер. с англ. Ю.И. Манин. — Под ред. М.М. Постникова. — М.: Иностранная литература, 1961. — 315 с. Книга М. Бальдассарри представляет собой по существу изложение наиболее важных аспектов абстрактной алгебраической геометрии. Эта интереснейшая отрасль современной математики, выросшая на стыке алгебры, топологии и дифференциальной геометрии, тесно связана как своими...
Монография. — Пер. с англ. Ю.И. Манин. — Под ред. М.М. Постникова. — М.: Иностранная литература, 1961. — 315 с. Книга М. Бальдассарри представляет собой по существу изложение наиболее важных аспектов абстрактной алгебраической геометрии. Эта интереснейшая отрасль современной математики, выросшая на стыке алгебры, топологии и дифференциальной геометрии, тесно связана как своими...
Монография. — М.: Московский центр непрерывного математического образования (МЦНМО), 2010. — 344 с. Эта книга, представляющая собой первый том двухтомной монографии, посвящена основам алгебраической геометрии комплексных многообразий и, шире, теории кэлеровых многообразий. Наряду с классическим «кэлеровым пакетом» (гармонические формы, разложение Ходжа, трудная теорема Лефшеца)...
М: Высшая школа экономики (ВШЭ), 2012. — 156 с. Целью изложенных шести лекций (Севастополь, 2 – 9 мая 2012 г.) является знакомство с проективной геометрией и классическими примерами проективных многообразий, а также с современным языком схем и простейшими геометрическими свойствами абстрактных алгебраических многообразий и морфизмов между ними. Курс задумывался как трамплин для...
Электронное издание. — М.: Московский центр непрерывного математического образования (МЦНМО), 2018. — 200 с. — ISBN 978-5-4439-3271-2. Книга представляет собой учебник по арифметической геометрии. Изложение строится вокруг понятия неразветвленной группы Брауэра алгебраического многообразия. Освещенные в книге темы включают когомологии Галуа, группы Брауэра, препятствия к...
Монография. — Перев. с англ. В.А. Исковский. — М.: Мир, 1982. — 496 с. Фундаментальная монография, написанная известными американскими учеными, содержит основы современной алгебраической геометрии, ее связи с другими отраслями математики, а также необходимый подготовительный аппарат. С присущим Ф. Гриффитсу мастерством вскрываются принципиальные идеи этой науки, которая в...
Монография. — Перев. с англ. В.А. Исковский. — М.: Мир, 1982. — 366 с. Фундаментальная монография, написанная известными американскими учеными, содержит основы современной алгебраической геометрии, ее связи с другими отраслями математики, а также необходимый подготовительный аппарат. С присущим Ф. Гриффитсу мастерством вскрываются принципиальные идеи этой науки, которая в...
Итоги науки и техн. Сер. Соврем. пробл. мат. Фундам. направления, 23, ВИНИТИ, М., 1988, 172–302.
Вводятся основные понятия алгебраической геометрии: алгебраического многообразия, морфизма, рационального отображения, гладкости, полноты. Для проективных многообразий излагаются степень многообразия, линейные системы, теория пересечений, многообразия Чжоу. В последней главе...
Алгебраическая геометрия-2. — М.: ВИНИТИ, 1989. — 130 с. — (Итоги науки и техн. Современные проблемы математики. Фундаментальные направления). Обзор посвящен изложению основных понятий и фактов о когомологиях алгебраических многообразий и применению их к геометрическим задачам.
Новосибирск: Сибирское отделение Российской академии наук (СО РАН), 2016. — 257 с. Алгебраическая геометрия над алгебраическими системами изложена с теоретико-модельных позиций. Показано, что большинство базовых понятий, результатов и идей классической алгебраической геометрии над полем допускают обобщение на случай произвольных алгебраических систем любой сигнатуры. При этом...
Підручник. — Київ: Київський національний університет імені Тараса Шевченка (КНУ), 2001. — 115 с. Афінні многовиди. Проективні та абстрактні многовиди. Теорія розмірності. Регулярні та особливі точки. Теорія перетинів.
М.: Московский центр непрерывного математического образования (МЦНМО), 2012. — 352 с. — ISBN 978-5-94057-935-9. В книгу вошли основные работы выдающегося алгебраического геометра В.А. Исковских по геометрии и арифметике алгебраических поверхностей. Эти работы оказали большое влияние на развитие отечественной и зарубежной алгебраической геометрии. Для студентов старших курсов,...
М.: Московский центр непрерывного математического образования (МЦНМО), 2012. — 356 с. — ISBN 9785940579359. В книгу вошли основные работы выдающегося алгебраического геометра В. А. Исковских по геометрии и арифметике алгебраических поверхностей. Эти работы оказали большое влияние на развитие отечественной и зарубежной алгебраической геометрии. Для студентов старших курсов,...
Учебное пособие. — М.: Московский государственный университет имени М.В. Ломоносова (МГУ), 1988. — 164 с. Лекция посвящены изложению теории трехмерных многообразий Фано. Приводится полная классификация таких многообразий с точностью до деформаций. Часть результатов, касающихся многообразий Фано индекса r>=2 и многообразий Фано с группой Динара Z, излагается подробно c полными...
Электронное издание. — М.: Московский центр непрерывного математического образования (МЦНМО), 2016. — 616 с. — ISBN 978-5-4439-2499-1. Книга является продолжением издания собрания математических трудов выдающегося русского математика, специалиста в области бирациональной алгебраической геометрии Василия Алексеевича Исковских. В нее включены работы по трехмерной бирациональной...
М.: ВИНИТИ, 1989. — Фрагмент: с. 131–263.
В обзоре представлена связная картина теории алгебраических поверхностей, разъяснены типичные постановки ее задач и описаны её основные методы. Изложение ведется на сравнительно элементарном уровне – доказательства даются лишь в тех случаях, когда они необходимы для выявления новых идей развития теории. В центре внимания авторов...
М.: Московский центр непрерывного математического образования (МЦНМО), 2019. — 272 с. — ISBN 978-5-4469-1365-0. В этой книге излагается теория комплексных алгебраических кривых и их семейств. Она содержит описание как классических результатов, так и недавних идей, связанных с геометрией пространства модулей кривых. Рекомендуется для студентов старших курсов математических и...
Пер. с англ. Ф. Ю. Попеленского. — Под ред. Ю.П. Соловьёва. — М.: Факториал Пресс, 2004. — 488 с. — ISBN 978-5-88688-069-4. В книге содержится систематическое изложение теории эллиптических кривых и модулярных форм, доведенное до самых новых результатов. Мастерски и доступно написанная, книга Э. Кнэппа вполне пригодна для первоначального ознакомления с этой удивительно богатой...
М.: Московский центр непрерывного математического образования (МЦНМО), 2012. — 576 с. — ISBN: 978-5-4439-0206-7. Книга посвящена теории зеркальной симметрии, которая возникла в последние годы и лежит на стыке квантовой теории поля и алгебраической геометрии в самом общем понимании этого понятия. Процесс создания математических основ теории зеркальной симметрии привёл к созданию...
М.: Московский центр непрерывного математического образования (МЦНМО), 2012. — 576 с. — ISBN: 978-5-4439-0206-7. Книга посвящена теории зеркальной симметрии, которая возникла в последние годы и лежит на стыке квантовой теории поля и алгебраической геометрии в самом общем понимании этого понятия. Процесс создания математических основ теории зеркальной симметрии привел к...
М.: Московский центр непрерывного математического образования (МЦНМО), 2012. — 576 с. — ISBN 978-5-4439-0206-7. Книга посвящена теории зеркальной симметрии, которая возникла в последние годы и лежит на стыке квантовой теории поля и алгебраической геометрии в самом общем понимании этого понятия. Процесс создания математических основ теории зеркальной симметрии привел к появлению...
Учебно-методическое пособие. — К.: Радянська школа, 1980. В пособии классифицированы задачи аффинной и метрической геометрии по курсу 7-10 классов, которые целесообразно решать методом векторов. Представлено более 100 задач с подробными методическими указаниями к их решению. Предназначается учителям математики.
Перев. с англ. С.А. Степанова. — М.: Наука, Главная редакция физико-математической литературы, 1984. — 312 с. Книга содержит достаточно полное изложение всех аспектов теории эллиптических функций и эллиптических кривых, начиная с классических и кончая самыми современными. Для специалистов в области теории функций и алгебраической геометрии.
Перев. с англ. Ю.И. Манина. — М.: Мир, 1971. — 299 с. Теория абелевых многообразий - один из самых ярких и важных в приложениях разделов алгебраической геометрии. Ее классический аспект связан с именами Абеля, Римана, Пуанкаре, а фундамент абстрактной теории заложен А. Вейлем. В этой книге впервые в мировой литературе изложены оба аспекта теории с единой точки зрения, с...
Учебное пособие. — Перевод с англ. — М.: Мир, 1979. — 256 с. Учебное пособие известного американского математика содержит основные факты алгебры, геометрии и анализа на комплексных алгебраических многообразиях. Автор стремился выработать у читателя геометрическую интуицию, которая необходима при переходе к абстрактной алгебраической геометрии. Книга будет полезна математикам, а...
М.: МЦНМО, 2007. — 296 с. — ISBN: 978-5-94057-195-7. На книге, которую вы держите в руках, было воспитано не одно поколение алгебраических геометров. Ее автор — не только один из крупнейших математиков XX века, но и блестящий педагог, книги которого неоднократно выходили в русских переводах и всегда пользовались заслуженной популярностью. В книге успешно решена неразрешимая на...
М.: Мир, 1968. — 235 с. Предлагаемая книга содержит прежде всего очень объемный очерк основных понятий теории схем и техники когомологий когерентных пучков на них. Далее, эта техника применяется к теории кривых и поверхностей, для которых строятся схемы Пикара и доказывается ряд фундаментальных алгебро-геометрических фактов. Книга трудна, но написана очень живо и на редкость...
Учебное пособие. — М.: Московский государственный университет имени М.В. Ломоносова (МГУ), 1970. — 133 с. В 1966—1968 гг. автор прочел на механико-математическом факультете МГУ двухгодовой курс лекций. Курс был задуман как введение в алгебраическую геометрию. Предлагаемая сейчас читателю небольшая книжка является первой главой задуманного учебника по алгебраической геометрии.
Учебное пособие. — М.: Московский государственный университет имени М.В. Ломоносова (МГУ), 1971. — 87 с. В 1966—1968 гг. автор прочел на механико-математическом факультете МГУ двухгодовой курс лекций. Курс был задуман как введение в алгебраическую геометрию; записки его первой части опубликованы годом раньше. Мне хотелось не только представить список некоторых основных понятий...
М.: Факториал Пресс, 2002. — 344 с. — ISBN 5-88688-057-7. Эта книга посвящена новому разделу математики, возникшему под влиянием математической физики (квантовой теории струн). Новые идеи этой теории оказали большое влияние на развитие дифференциальной, симплектической и алгебраической геометрии последнего десятилетия. Развитие этих дисциплин явилось, в свою очередь,...
М.: Факториал Пресс, 2002. — 344 с. — ISBN 5-88688-057-7. Эта книга посвящена новому разделу математики, возникшему под влиянием математической физики (квантовой теории струн). Новые идеи этой теории оказали большое влияние на развитие дифференциальной, симплектической и алгебраической геометрии последнего десятилетия. Развитие этих дисциплин явилось, в свою очередь,...
Монография. — М.: Мир, 1983. Понятие этальных когомологий было впервые введено в работах А. Гротендика и М. Артина, посвященных алгебраической геометрии. Данная книга является первой монографией, посвященной этому разделу современной математики. Этальные морфизмы. Теория пучков. Когомологии. Группа Брауэра. Когомологии кривых и поверхностей. Основные теоремы.
М.: Московский центр непрерывного математического образования (МЦНМО), 2003. — 176 с: ил. — ISBN: 5-94057-058-5. Книга посвящена исследованию топологической структуры пространств модулей римановых поверхностей и близких к ним пространств: вещественных алгебраических кривых, пространств отображений и супераналогов всех этих пространств. Исследованы также важные для приложений...
М.: Наука, 1965. — (Труды математического института им. В. А. Стеклова LXXV). Настоящая книга написана на основе докладов на семинаре по теории алгебраических поверхностей, который работал в 1961—1962 и 1962—1963 гг. под руководством И. Р. Шафаревича. Тексты докладов были затем переработаны, а некоторые части написаны заново. Классические результаты, излагаемые в этой книге,...
Монография. — М.: Московский центр непрерывного математического образования (МЦНМО), 2010. — 295 с. — ISBN: 9785940576211, 5940576214. Книга является современной монографией по теории абелевых многообразий (как над комплексными числами, так и над произвольным полем). Освещены, в частности, такие вопросы, как тэта-функции, связь с группой Гейзенберга, преобразование Фурье-Мукаи.
Учебное пособие. — М.: Московский государственный университет имени М.В. Ломоносова (МГУ), 2002. — 38 c. Лекции, читанные в Институте теоретической и экспериментальной физики (ИТЭФ) в мае-июне 2002 г. Пособие подготовлено на механико-математический факультете, на кафедре высшей алгебры. Вводная лекция. Бирациональные преобразования, минимальные модели, дивизоры и линейные...
М.: Московский центр непрерывного математического образования (МЦНМО), 2009. — 128 с. — ISBN: 978-5-94057-428-6. Книга посвящена важному разделу алгебраической геометрии — теории особенностей алгебраических многообразий. Она состоит из двух практически независимых друг от друга частей. В первой части обсуждается доказательство теоремы о разрешении особенностей, ослабленной...
М.: Математический институт имени В.А. Стеклова (МИАН), 2015. — 76 с. — (Лекционные курсы НОЦ. Выпуск 24). Серия «Лекционные курсы НОЦ» — рецензируемое продолжающееся издание Математического института им. В. А. Стеклова РАН. В серии «Лекционные курсы НОЦ» публикуются материалы специальных курсов, прочитанных в Математическом институте им. В. А. Стеклова Российской академии наук...
М.: Математический институт имени В.А. Стеклова (МИАН), 2022. — 151 с. Лекционные курсы НОЦ, выпуск 31 Многообразия Фано — это проективные алгебраические многообразия с обильным антиканоническим классом. Классификация таких многообразий была начата в работах Джино Фано . Более точно, он рассматривал трехмерные многообразия, вложенные в проективное пространство, у которых кривые...
Пер. с англ. Б.З. Шапиро. — М.: Мир, 1991. — 151 с. — ISBN 5-03-001792-5. — (Современная математика. Вводные курсы). Автор, известный английский математик, поставил себе целью преодолеть страх математиков перед алгебраической геометрией, подобный страху не математиков перед математикой. Примеры, задачи, рисунки и мотивировка занимают в книге больше места, чем формальный аппарат...
Пер. с англ. Б.З. Шапиро. — М.: Мир, 1991. — 151 с. — (Современная математика. Вводные курсы). — ISBN 5-03-001792-5. Автор, известный английский математик, поставил себе целью преодолеть страх математиков перед алгебраической геометрией, подобный страху не математиков перед математикой. Примеры, задачи, рисунки и мотивировка занимают в книге больше места, чем формальный аппарат...
Перевод с фр. И.В. Додгачева. — Под ред. С.П. Демушкина. — М.: Мир, 1968. — 290 с. Книга известного французского математика Ж. Серра стала одной из классических книг по алгебраической геометрии. Она не требует больших предварительных знаний и вводит читателя в круг современных вопросов. С большим педагогическим мастерством в ней излагается ряд основных понятий алгебраической...
Перевод с фр. И.В. Додгачева. — Под ред. С.П. Демушкина. — М.: Мир, 1968. — 290 с. Книга известного французского математика - одна из классических книг по алгебраической геометрии. В ней излагается ряд основных понятий алгебраической геометрии: алгебраические кривые и поверхности, теорема Римана - Роха, Якобиевы многообразия кривых, отображения кривой в коммутативную группу,...
Перевод с англ. А.И. Узкова. — М.: Иностранная литература, 1952. — 236 с. Книга Уокера является введением в алгебраическую геометрию в той ее части, которая связана с кривыми линиями. Две первые главы содержат все сведения из алгебры и проективной геометрии, необходимые для дальнейшего чтения книги и делают ее доступной студенту второго курса университета. В третьей главе...
Перевод с англ. А.И. Узкова. — М.: Иностранная литература, 1952. — 236 с. Книга Уокера является введением в алгебраическую геометрию в той ее части, которая связана с кривыми линиями. Две первые главы содержат все сведения из алгебры и проективной геометрии, необходимые для дальнейшего чтения книги и делают ее доступной студенту второго курса университета. В третьей главе...
Монография. — Пер. с англ. В.И. Данилова. — М.: Мир, 1989. — 583 с. — ISBN 5-03-000849-7. Книга известного американского математика представляет собой по существу первое изложение теории пересечений алгебраических циклов на алгебраических многообразиях. В ней отражены как новейшие результаты и методы, так и классические достижения. Каждое продвижение в теории иллюстрируется...
Монография. — Пер. с англ. В.И. Данилова. — М.: Мир, 1989. — 583 с. — ISBN 5-03-000849-7. Книга известного американского математика представляет собой по существу первое изложение теории пересечений алгебраических циклов на алгебраических многообразиях. В ней отражены как новейшие результаты и методы, так и классические достижения. Каждое продвижение в теории иллюстрируется...
М.: Московский центр непрерывного математического образования (МЦНМО), 2005. — 400 с. Книга представляет собой геометрическое введение в алгебраическую геометрию, написанное одним из крупнейших специалистов в этой области математики. Основное внимание уделено не основаниям предмета, а конкретным примерам и более "геометрическим" его разделам. Благодаря этому неспециалист...
М.: Московский центр непрерывного математического образования (МЦНМО), 2009. — 400 с. — ISBN 5-94057-084-4. Книга представляет собой геометрическое введение в алгебраическую геометрию, написанное одним из крупнейших специалистов в этой области математики. Основное внимание уделено не основаниям предмета, а конкретным примерам и более «геометрическим» его разделам. Благодаря...
Пер. с англ. — М.: Мир, Научный мир, 2004. — 448 с. — ISBN 5-03-003399-8 (Мир). — ISBN 5-89176-242-0 (Научный мир). Изучение геометрии пространства модулей кривых - одно из наиболее активно развивающихся направлений алгебраической геометрии. Книга известных американских математиков содержит доступное для студентов изложение главных результатов в этой области, которые ранее...
Монография. — Перевод с англ. В.А. Исковских. — М.: Мир, 1981. — 580 с. Монография учебного характера по алгебраической геометрии, написанная с большим педагогическим мастерством известным американским ученым. Материал излагается на современном языке теории схем и когомологий. Представлено более 400 задач и упражнений для самостоятельной работы. Для математиков, интересующихся...
Монография. — Перевод с англ. В.А. Исковских. — М.: Мир, 1981. — 580 с. Монография учебного характера по алгебраической геометрии, написанная с большим педагогическим мастерством известным американским ученым. Материал излагается на современном языке теории схем и когомологий. Представлено более 400 задач и упражнений для самостоятельной работы. Для математиков, интересующихся...
Перев. с англ. А.И. Узкова. — М.: Издательство иностранной литературы, 1954. — 462 c. Первый том содержит алгебраическое введение и теорию проективных пространств. Геометрия алгебраических многообразий высших размерностей является естественным развитием теории алгебраических кривых и поверхностей. Ее можно рассматривать также как геометрическую теорию систем алгебраических...
Перев. с англ. А.И. Узкова. — М.: Издательство иностранной литературы, 1954. — 429 с. В этом томе излагаются основные методы теории алгебраических многообразий в n-мерном пространстве. В нем даются также приложения этих методов к некоторым из наиболее важных многообразий и основы бирациональной геометрии. Общая теория алгебраических многообразий в проективном пространстве....
Перев. с англ. А.И. Узкова. — М.: Издательство иностранной литературы, 1955. — 374 c. Целью этого тома является изложение современных алгебраических методов, полезных при исследованиях в области бирациональной геометрии алгебраических многообразий. Подобное изложение уже опубликовано Вейлем в его книге. Когда будут опубликованы лекции Зарисского, прочитанные в Коллоквиуме...
3-е изд., доп. — М.: Московский центр непрерывного математического образования (МЦНМО), 2007. — 589 с.: ил. — ISBN: 978-5-94057-085-1 Книга посвящена систематическому изложению основ алгебраической геометрии. Дает общее представление об этой области и основу для чтения более специальной литературы. Изложение иллюстрировано большим числом примеров и приложений. Книга...
3-е изд., доп. — М.: Московский центр непрерывного математического образования (МЦНМО), 2007. — 589 с.: ил. — ISBN: 978-5-94057-085-1. Книга посвящена систематическому изложению основ алгебраической геометрии. Дает общее представление об этой области и основу для чтения более специальной литературы. Изложение иллюстрировано большим числом примеров и приложений. Книга...
Изд. 2-е, перераб. и доп. — В 2-х т. — М.: Наука, Главная редакция физико-математической литературы, 1988. — 352 с. — ISBN: 5-02-014412-4. Посвящена систематическому изложению основ алгебраической геометрии. Дает общее представление об этой области и основу для чтения более специальной литературы. Изложение иллюстрировано большим числом примеров и приложений. Соответствует...
Изд. 2-е, перераб. и доп. — В 2-х т. — М.: Наука, Главная редакция физико-математической литературы, 1988. — 304 с. — ISBN 5-02-014412-4. Соответствует второй и третьей частям первого издания (1972 г. ). Содержит основные понятия теории пучков и схем, а также теорию алгебраических многообразий над полем комплексных чисел и ее связи с топологией и теорией аналитических...
Только вот подраздел находится не в своем родительском разделе. Он должен находиться внутри раздела "Общая алгебра". Алгебраическая геометрия - алгебраическая дисциплина (изучает алгебраические многообразия). Слово "геометрия" в названии дисциплины дань составу изучаемых объектов ранней истории дисциплины - геометрическим объектам (алгебраические кривые: прямые, конические сечения, кубики (такие как эллиптическая кривая), алгебраические поверхности и т.д.), заданные как множества решений систем алгебраических уравнений. В целом АГ большинством математиков относится к алгебре, спецкурсы по АГ читаются на кафедрах алгебры (я сам слушал такой курс в исполнении И. Шафаревича на кафедре высшей алгебры мех-мата МГУ). В УДК АГ располагается внутри Алгебры: 512 Алгебра, 512.7 Алгебраическая геометрия (см. http://teacode.com/online/udc/51/512.html ). Та же картина в ББК (Библиотечно-библиографическая классификация): 22.14 Алгебра, 22.147 Алгебраическая геометрия. В Mathematics Subject Classification (используемой в крупнейших в мире математических реферативных базах Mathematical Reviews и Zentralblatt MATH, а также в большинстве западных математических журналах): Discrete mathematics/algebra [Study of structure of mathematical abstractions] - первый уровень 05: Combinatorics 06: Order theory 08: General algebraic systems 11: Number theory 12: Field theory and polynomials 13: Commutative rings and algebras 14: Algebraic geometry 15: Linear and multilinear algebra; matrix theory 16: Associative rings and associative algebras 17: Non-associative rings and non-associative algebras 18: Category theory; homological algebra 19: K-theory 20: Group theory and generalizations 22: Topological groups, Lie groups, and analysis upon them . . . . . . . . . . . . . Geometry and topology [Study of space] - первый уровень 51: Geometry 52: Convex geometry and discrete geometry 53: Differential geometry 54: General topology 55: Algebraic topology 57: Manifolds 58: Global analysis, analysis on manifolds (including infinite-dimensional holomorphy). (см. https://en.wikipedia.org/wiki/Mathematics_Subject_Classification )
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Он должен находиться внутри раздела "Общая алгебра".
Алгебраическая геометрия - алгебраическая дисциплина (изучает алгебраические многообразия). Слово "геометрия" в названии дисциплины дань составу изучаемых объектов ранней истории дисциплины - геометрическим объектам (алгебраические кривые: прямые, конические сечения, кубики (такие как эллиптическая кривая), алгебраические поверхности и т.д.), заданные как множества решений систем алгебраических уравнений.
В целом АГ большинством математиков относится к алгебре, спецкурсы по АГ читаются на кафедрах алгебры (я сам слушал такой курс в исполнении И. Шафаревича на кафедре высшей алгебры мех-мата МГУ).
В УДК АГ располагается внутри Алгебры: 512 Алгебра, 512.7 Алгебраическая геометрия (см. http://teacode.com/online/udc/51/512.html ).
Та же картина в ББК (Библиотечно-библиографическая классификация): 22.14 Алгебра, 22.147 Алгебраическая геометрия.
В Mathematics Subject Classification (используемой в крупнейших в мире математических реферативных базах Mathematical Reviews и Zentralblatt MATH, а также в большинстве западных математических журналах):
Discrete mathematics/algebra [Study of structure of mathematical abstractions] - первый уровень
05: Combinatorics
06: Order theory
08: General algebraic systems
11: Number theory
12: Field theory and polynomials
13: Commutative rings and algebras
14: Algebraic geometry
15: Linear and multilinear algebra; matrix theory
16: Associative rings and associative algebras
17: Non-associative rings and non-associative algebras
18: Category theory; homological algebra
19: K-theory
20: Group theory and generalizations
22: Topological groups, Lie groups, and analysis upon them
. . . . . . . . . . . . .
Geometry and topology [Study of space] - первый уровень
51: Geometry
52: Convex geometry and discrete geometry
53: Differential geometry
54: General topology
55: Algebraic topology
57: Manifolds
58: Global analysis, analysis on manifolds (including infinite-dimensional holomorphy).
(см. https://en.wikipedia.org/wiki/Mathematics_Subject_Classification )
Теперь людям гораздо легче будет ориентироваться в разделе Высшая геометрия и быстрее искать нужную литературу. Слава Богу!
Да благословит Господь Вас, ваших родных, близких, друзей и знакомых.
С уважением, благодарностью и благословением,