Modular forms of one variable 


33 c 

djvu 1.2 Мб 
Infinite dimensional Grassmannians 
Abbondandolo A. 
2003 г 
27 c 

djvu 194 Кб 
Toroidal Groups : Line Bundles, Cohomology and QuasiAbelian Varieties (Lecture Notes in Mathematics) 
Abe Y., Kopfermann K. 
2001 г 
120 c 

djvu 932 Кб 
Toroidal groups are the connecting link between torus groups and any complex Lie groups. Показать полностьюToroidal groups are the connecting link between torus groups and any complex Lie groups. Many properties of complex Lie groups such as the pseudoconvexity and cohomology are determined by their maximal toroidal subgroups. QuasiAbelian varieties are meromorphically separable toroidal groups. They are the natural generalisation of the Abelian varieties. Nevertheless, their behavior can be completely different as the wild groups show. 
Introduction to Grothendieck duality theory 
Altman A., Kleiman S. 
1970 г 
96 c 

djvu 1 021 Кб 
Geometry of Algebraic Curves. Volume 1 
Arbarello E., Harris J., James R. 
1984 г 
386 c 

djvu 4.7 Мб 
These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and selfcontained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Показать полностьюThese books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and selfcontained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, Of course, discuss applications of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves). 
Algebraic spaces 
Artin M. 
1971 г 
39 c 

djvu 364 Кб 
These notes are based on lectures given at Yale University in the spring of 1969. Показать полностьюThese notes are based on lectures given at Yale University in the spring of 1969. Their object is to show how algebraic functions can be used systematically to develop certain notions of algebraic geometry, which are usually treated by rational functions by using projective methods. The global structure which is natural in this context is that of an algebraic space—a space obtained by gluing together sheets of affine schemes by means of algebraic functions. 
Theorie des topos et cohomologie etale des schemas (SGA 4. III.) 
Artin M., Grothendieck A., Verdier J.L. 
1972 г 
646 c 

djvu 8 Мб 
Theorie des topos et cohomologie etale des schemas (SGA 4. I.) 
Artin M., Grothendieck A., Verdier J.L. 
1972 г 
545 c 

djvu 8 Мб 
Theorie des topos et cohomologie etale des schemas (SGA 4. II.) 
Artin M., Grothendieck A., Verdier J.L. 
1972 г 
424 c 

djvu 6 Мб 
Arithmetic and Geometry: Papers Dedicated to I.R. Shafarevich on the Occasion of His Sixtieth Birthday. Volume 2. Geometry 
Artin M., Tate J. (eds.) 
1983 г 
248 c 

djvu 9 Мб 
Arithmetic and Geometry: Papers Dedicated to I.R. Shafarevich on the Occasion of His Sixtieth Birthday. Voleme 1. Arithmetic 
Artin M., Tate J. (eds.) 
1983 г 
364 c 

djvu 3.8 Мб 
Igor Rostislavovich Shafarevich has made outstanding contributions in number theory, algebra, and algebraic geometry. Показать полностьюIgor Rostislavovich Shafarevich has made outstanding contributions in number theory, algebra, and algebraic geometry. The flourishing of these fields in Moscow since World War II owes much to his influence. We hope these papers, collected for his sixtieth birthday, will indicate to him the great respect and admiration which mathematicians throughout the world have for him. 
The topology of torus actions on symplectic manifolds 
Audin M. 
1991 г 
181 c 

djvu 1.3 Мб 
This book comes from a course I gave in Strasbourg in 198889. In the audience were in particular Julien Duval, Santiago Lopez de Medrano and Marcus Slupinski who helped me by their questions to understand many of the points I was supposed to be explaining. Показать полностьюThis book comes from a course I gave in Strasbourg in 198889. In the audience were in particular Julien Duval, Santiago Lopez de Medrano and Marcus Slupinski who helped me by their questions to understand many of the points I was supposed to be explaining. There were genuine students as well who, refusing to understand what I was badly explaining, suggested many improvements. I am thinking in particular of J. Fougeront, P. Gaucher, Li Jie and J.M. Rinkel. 
Compact complex surfaces 
Barth W., Peters C., Van de Ven A. 
1984 г 
161 c 

djvu 3 Мб 
Early versions of parts of this work date back to the midsixties, when the third author started to write a book on surfaces. Показать полностьюEarly versions of parts of this work date back to the midsixties, when the third author started to write a book on surfaces. But for several reasons, in particular the appearance of afareviUs book, he postponed the project. It was revived about ten years later, when all three authors were in Leiden. It is impossible to cover in one book the vast and rapidly developing theory of surfaces. Choices have to be made, with respect to content as well as to presentation. We have chosen for a complexanalytic point of view; this distinguishes our text from most of the existing treatments. Relations with the case of characteristic p are not discussed. We hope to have succeeded in writing a readable book; a book that can be used by nonspecialists. The specialist will find very little that is new to him anyhow. 
Complex Algebraic Surfaces 
Beauville A. 
1996 г 
132 c 

djv 878 Кб 
Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. Показать полностьюDeveloped over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor Beauville gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research. 
Algebraic geometry angers 1979 
Beauville A. (ed.) 
1980 г 
323 c 

djvu 3.1 Мб 
Faisceany pervers 
Beilinson A., Bernstein J., Deligne P. 
1982 г 
173 c 

djvu 1.8 Мб 
Theorie des reductions et theoreme de RiemannRoch (SGA 6) 
Berthelot P., Grothendieck A., Illusie L. 
1971 г 
700 c 

djvu 11 Мб 
Complex Abelian Varieties 
Birkenhake C., Lange H. 
2004 г 
655 c 

djvu 4.4 Мб 
May be used as an introduction or reference. Covers the theory of abelian varieties over the field of complex numbers. Показать полностьюMay be used as an introduction or reference. Covers the theory of abelian varieties over the field of complex numbers. Topics include projective embeddings of an abelian variety including their equations and geometric properties, special results of Jacobians and Prym varieties allowing applications to the theory of algebraic curves, complex tori, cohomology of line bundles, and constructions of several moduli spaces of abelian varieties with additional structure. Problems follow each chapter. 
Alexandre Grothendieck’s EGA V 
Blass P., Blass J. 

112 c 

djvu 1 021 Кб 
Real Algebraic Geometry 
Bochnak J., Coste M., Roy M.F. 
1998 г 
220 c 

djvu 6 Мб 
The present volume is a translation, revision and updating of our book (published in French) with the title "Geometrie Algebrique Relle". Since its publication in 1987 the theory has made advances in several directions. Показать полностьюThe present volume is a translation, revision and updating of our book (published in French) with the title "Geometrie Algebrique Relle". Since its publication in 1987 the theory has made advances in several directions. There have also been new insights into material already in the French edition. Many of these advances and insights have been incorporated in this English version of the book, so that it may be viewed as being substantially different from the original. 
Algebraic DModules 
Borel A. 
1986 г 
355 c 

djvu 2.4 Мб 
Presented here are recent developments in the algebraic theory of Dmodules. Показать полностьюPresented here are recent developments in the algebraic theory of Dmodules. The book contains an exposition of the basic notions and operations of Dmodules, of special features of coherent, holonomic, and regular holonomic Dmodules, and of the RiemannHilbert correspondence. The theory of Algebraic Dmodules has found remarkable applications outside of analysis proper, in particular to infinite dimensional representations of semisimple Lie groups, to representations of Weyl groups, and to algebraic geometry. 
Homotopy limits, completions and localizations 
Bousfield A., Kan D. 
1972 г 
348 c 

djvu 3 Мб 
The main purpose of part I of these notes is to develop for a ring R a functional notion of Rcompletion of a space X. For R=Zp and X subject to usual finiteness condition, the Rcompletion coincides up to homotopy, with the pprofinite completion of Quillen and Sullivan; for R a subring of the rationals, the Rcompletion coincides up to homotopy, with the localizations of Quillen, Sullivan and others. Показать полностьюThe main purpose of part I of these notes is to develop for a ring R a functional notion of Rcompletion of a space X. For R=Zp and X subject to usual finiteness condition, the Rcompletion coincides up to homotopy, with the pprofinite completion of Quillen and Sullivan; for R a subring of the rationals, the Rcompletion coincides up to homotopy, with the localizations of Quillen, Sullivan and others. In part II of these notes, the authors have assembled some results on towers of fibrations, cosimplicial spaces and homotopy limits which were needed in the discussions of part I, but which are of some interest in themselves. 
Algebraic Geometry 
Bump D. 
1999 г 
250 c 

djvu 1.9 Мб 
A text for a oneyear course at the graduate level, for students with substantial background in algebra. Показать полностьюA text for a oneyear course at the graduate level, for students with substantial background in algebra. Eight chapters contain material applicable to varieties of every dimension, and six chapters contain material which is particular to the theory of curves. Material considers irreducible varieties over an algebraically closed field, except in one chapter, which works over a finite field. Coverage includes the extension theorem, maps of affine varieties, complete nonsingular curves, and the RiemannRoch theory. Intersection theory is not covered. Includes chapter exercises. The author teaches mathematics at Stanford University. 
Lectures on Elliptic Curves 
Cassels J.W.S. 
1991 г 
143 c 

djvu 740 Кб 
The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. Показать полностьюThe study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the MordellWei finite basis theorem, points of finite order (NagellLutz), etc. The treatment is structured by the localglobal standpoint and culminates in the description of the TateShafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the "Riemann hypothesis for function fields") and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The padic numbers are introduced from scratch. Many examples and exercises are included for the reader, and those new to elliptic curves, whether they are graduate students or specialists from other fields, will find this a valuable introduction. 
Algebre commutative et introduction a geometrie algebrique 
ChambertLoir A. 
1998 г 
83 c 

djvu 770 Кб 
This graduate course has two faces: algebra and geometry. Indeed, we study simultaneously loci of points defined by polynomial equations and algebras of finite type over a field. Показать полностьюThis graduate course has two faces: algebra and geometry. Indeed, we study simultaneously loci of points defined by polynomial equations and algebras of finite type over a field. We shall show on examples (Hilbert’s Nullstellensatz, dimension theory, regularity) how these are two faces of a single head and how both geometrie and algebraic aspects enlight the one the other. 
Algebraic surfaces 
Chen J. 
2003 г 
34 c 

djvu 369 Кб 
In this course, we are going to give a quick introduction to the theory of algebraic surfaces, for students who might had little experience with algebraic geometry. Показать полностьюIn this course, we are going to give a quick introduction to the theory of algebraic surfaces, for students who might had little experience with algebraic geometry. With minimal model program in mind, our purpose is to give a modern treatment of surface theory, and leave the classical classification theory as an application of general machinary. 
Trace formula in noncommutative geometry and the zeros of the Riemann zeta function 
Connes A. 
1997 г 
29 c 

djvu 457 Кб 
Abstrac: We give a spectral interpretation of the critical zeros of the Riemann zeta function, and a geometric interpretation of the explicit formulas of number theory as a trace formula on a noncommutative space. Показать полностьюAbstrac: We give a spectral interpretation of the critical zeros of the Riemann zeta function, and a geometric interpretation of the explicit formulas of number theory as a trace formula on a noncommutative space. This reduces the Riemann hypothesis to the validity of the trace formula. 
Noncommutative geometry 
Connes A. 
1994 г 
661 c 

djvu 6 Мб 
This English version of the pathbreaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Показать полностьюThis English version of the pathbreaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields. Key Features * First full treatment of the subject and its applications * Written by the pioneer of this field * Broad applications in mathematics * Of interest across most fields * Ideal as an introduction and survey * Examples treated include: @subbul* the space of Penrose tilings * the space of leaves of a foliation * the space of irreducible unitary representations of a discrete group * the phase space in quantum mechanics * the Brillouin zone in the quantum Hall effect * A model of space time 
Grothendieck duality and base charge 
Conrad B. 
2000 г 
300 c 

djvu 2.3 Мб 
Enriques surfaces I 
Cossec F., Dolgachev I. 
1989 г 
203 c 

djvu 2 Мб 
This is the first of two volumes representing the ourrent state of knowledge about Enriques surfaces whioh oooupy one of the olasses in the olassifioation of algebraic surfaces. Показать полностьюThis is the first of two volumes representing the ourrent state of knowledge about Enriques surfaces whioh oooupy one of the olasses in the olassifioation of algebraic surfaces. Recent improvements in our understanding of algebraio surfaces over fields of positive oharaoteristio allowed us to approaoh the subject from a completely geometdo point of view although heavily relying on algebraio methods. Some of the techniques presented in this book oan be applied to the study of algebraic surfaces of other types. We hope that it will make this book of partioular interest to a wider range of researoh mathematioians and graduate students. 
Mirror symmetry and algebraic geometry 
Cox D., Katz S. 
1999 г 
469 c 

djvu 7 Мб 
Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in fourdimensional projective space. Показать полностьюMirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in fourdimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is the first completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, Kähler geometry, moduli of stable maps, CalabiYau manifolds, quantum cohomology, GromovWitten invariants, and the mirror theorem. 
Cyclic Homology in NonCommutative Geometry 
Cuntz J., Skandalis G., Tsygan B. 
2004 г 
137 c 

djvu 1.2 Мб 
This volume contains contributions by three authors and treats aspects of noncommutative geometry that are related to cyclic homology. Показать полностьюThis volume contains contributions by three authors and treats aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different and complementary points of view. The connections between topological (bivariant) Ktheory and cyclic theory via generalized Cherncharacters are discussed in detail. This includes an outline of a framework for bivariant Ktheory on a category of locally convex algebras. On the other hand, cyclic theory is the natural setting for a variety of general index theorems. A survey of such index theorems (including the abstract index theorems of ConnesMoscovici and of BresslerNestTsygan) is given and the concepts and ideas involved in the proof of these theorems are explained. 
Monomialization of morphisms from 3folds to surfaces 
Cutkosky S.D. 
2002 г 
223 c 

djvu 1.2 Мб 
Geometry of toric varieties 
Danilov V.I. 
1978 г 
30 c 

djvu 648 Кб 
HigherDimensional Algebraic Geometry 
Debarre O. 
2001 г 
233 c 

djvu 2.8 Мб 
HigherDimensional Algebraic Geometry studies the classification theory of algebraic varieties. Показать полностьюHigherDimensional Algebraic Geometry studies the classification theory of algebraic varieties. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The author’s goal is to provide an easily accessible introduction to the subject. Based on lectures given at Harvard University, the book begins with preparatory and standard definitions and results, moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps toward Mori’s minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. 
Groupes de monodromie en geometrie algebrique (SGA 7/1, 7/2 (LNM 288,340)) 
Deligne P., Katz N. 
1973 г 
448 c 

djvu 4.7 Мб 
Complex Analytic and Differential Geometry 
Demailly JP. 
1997 г 
518 c 

djvu 1.8 Мб 
Introduction to algebraic geometry and algebraic groups 
Demazure M., Gabriel P. 
1980 г 
357 c 

djvu 4 Мб 
An accessible text introducing algebraic geometry 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 geometries from first principles. Показать полностьюAn accessible text introducing algebraic geometry 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 geometries from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups and Lie type. The text covers the conjugacy of borel subgroups and maximal tori, the theory of algebraic groups with a BNpair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions, and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new proofs. The text uses algebraic groups as the main examples, including worked out examples, instructuve exercises, as well as bibliographical and historical remarks. 
Seminaire de Geometrie Algebrique (Tome 2). Groupes de type multiplicatif, et structure des schemas en groupes generaux. (SGA 3/2, LNM 152) 
Demazure M., Grothendieck A. 
1970 г 
661 c 

djvu 14 Мб 
Seminaire de Geometrie Algebrique (Tome 3). Structures des schemas en groupes reductifs (SGA 3/3, LNM 153) 
Demazure M., Grothendieck A. 
1970 г 
529 c 

djvu 9 Мб 
Seminaire de Geometrie Algebrique (Tome 1). Properties generales de schemas et groupes (SGA 3/1, LNM 151) 
Demazure M., Grothendieck A. 
1970 г 
564 c 

djvu 10 Мб 
Cohomologie etale (SGA 4.5 (LNM 569)) 
Dold A., Eckmann B. (eds.) 
1977 г 
315 c 

djvu 3.1 Мб 
Cohomologie ladique et fonctions L (SGA 5) 
Dold A., Eckmann B. (eds.) 
1977 г 
496 c 

djvu 4 Мб 
Topics in classical algebraic geometry. Part 1 
Dolgachev I. 
2003 г 
184 c 

gz 438 Кб 
Introduction to algebraic geometry 
Dolgachev I. 

143 c 

gz 502 Кб 
Topics in classical algebraic geometry. Part 2 
Dolgachev I. 
2003 г 
23 c 

gz 80 Кб 
Lectures on Invariant Theory 
Dolgachev I. 
2003 г 
220 c 

pdf 901 Кб 
This introduction to the main ideas of algebraic and geometric invariant theory assumes only a minimal background in algebraic geometry, algebra and representation theory. Показать полностьюThis introduction to the main ideas of algebraic and geometric invariant theory 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 finitegeneratedness of the algebra of invariants, and the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples that originate in classical algebraic geometry. Written in an accessible style with many examples and exercises, the book offers a novel discussion of possible linearizations of actions and the variation of quotients under the change of linearization. 
Lectures on Modular Forms 
Dolgachev I. 
1997 г 
147 c 

gz 456 Кб 
The Geometry of FourManifolds 
Donaldson K., Kronheimer P.B. 
1990 г 
222 c 

djvu 3.9 Мб 
The last ten years have seen rapid advances in the understanding of differentiable fourmanifolds, not least of which has been the discovery of new ‘exotic’ manifolds. Показать полностьюThe last ten years have seen rapid advances in the understanding of differentiable fourmanifolds, not least of which has been the discovery of new ‘exotic’ manifolds. These results have had farreaching consequences in geometry, topology, and mathematical physics, and have proven to be a mainspring of current mathematical research. This book provides a lucid and accessible account of the modern study of the geometry of fourmanifolds. Consequently, it will be required reading for all those mathematicians and theoretical physicists whose research touches on this topic. The authors present both a thorough treatment of the main lines of these developments in fourmanifold topology — notably the definition of new invariants of fourmanifolds — and also a wideranging treatment of relevant topics from geometry and global analysis. All of the main theorems about YangMills instantons on fourmanifolds are proven in detail. On the geometric side, the book contains a new proof of the classification of instantons on the foursphere, together with an extensive discussion of the differential geometry of holomorphic vector bundles. At the end of the book the different strands of the theory are brought together in the proofs of results which settle longstanding problems in fourmanifolds topology and which are close to the frontiers of current research. Coauthor Donaldson is the 1994 corecipient of the prestigious Crafoord Prize. 
Commutative algebra with a view toward algebraic geometry 
Eisenbud D. 
1995 г 
797 c 

djvu 7 Мб 
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. Показать полностьюCommutative 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, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self contained. Novel results and presentations are scattered throughout the text. 