Complex Tori

Author : Olivier Debarre
Publisher : American Mathematical Soc.
Page : 124 pages
File Size : 48,7 Mb
Release : 2005
Category : Mathematics
ISBN : 0821831658

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Complex Tori and Abelian Varieties by Olivier Debarre Pdf

This graduate-level textbook introduces the classical theory of complex tori and abelian varieties, while presenting in parallel more modern aspects of complex algebraic and analytic geometry. Beginning with complex elliptic curves, the book moves on to the higher-dimensional case, giving characterizations from different points of view of those complex tori which are abelian varieties, i.e., those that can be holomorphically embedded in a projective space. This allows, on the one hand, for illuminating the computations of nineteenth-century mathematicians, and on the other, familiarizing readers with more recent theories. Complex tori are ideal in this respect: One can perform "hands-on" computations without the theory being totally trivial. Standard theorems about abelian varieties are proved, and moduli spaces are discussed. Recent results on the geometry and topology of some subvarieties of a complex torus are also included. The book contains numerous examples and exercises. It is a very good starting point for studying algebraic geometry, suitable for graduate students and researchers interested in algebra and algebraic geometry. Information for our distributors: SMF members are entitled to AMS member discounts.

Author : Herbert Lange,Christina Birkenhake
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461215660

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Complex Tori by Herbert Lange,Christina Birkenhake Pdf

A complex torus is a connected compact complex Lie group. Any complex 9 9 torus is of the form X =

Author : B.A. Dubrovin,A.T. Fomenko,S.P. Novikov
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 55,6 Mb
Release : 1985-08-05
Category : Mathematics
ISBN : 9780387961620

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Modern Geometry— Methods and Applications by B.A. Dubrovin,A.T. Fomenko,S.P. Novikov Pdf

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.

Author : Dale Husemöller
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 54,6 Mb
Release : 2006-06-06
Category : Mathematics
ISBN : 9780387215778

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Elliptic Curves by Dale Husemöller Pdf

First Edition sold over 2500 copies in the Americas; New Edition contains three new chapters and two new appendices

Author : Athanase Papadopoulos
Publisher : Springer Nature
Page : 469 pages
File Size : 51,8 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9783030866952

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Surveys in Geometry I by Athanase Papadopoulos Pdf

The volume consists of a set of surveys on geometry in the broad sense. The goal is to present a certain number of research topics in a non-technical and appealing manner. The topics surveyed include spherical geometry, the geometry of finite-dimensional normed spaces, metric geometry (Bishop—Gromov type inequalities in Gromov-hyperbolic spaces), convexity theory and inequalities involving volumes and mixed volumes of convex bodies, 4-dimensional topology, Teichmüller spaces and mapping class groups actions, translation surfaces and their dynamics, and complex higher-dimensional geometry. Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to current research trends in geometry.

Author : Tiago J. Fonseca
Publisher : American Mathematical Society
Page : 158 pages
File Size : 51,9 Mb
Release : 2023-01-18
Category : Mathematics
ISBN : 9781470460198

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Higher Ramanujan Equations and Periods of Abelian Varieties by Tiago J. Fonseca Pdf

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Author : Alfonso Di Bartolo,Giovanni Falcone,Peter Plaumann,Karl Strambach
Publisher : Springer
Page : 212 pages
File Size : 51,6 Mb
Release : 2008-04-03
Category : Mathematics
ISBN : 9783540785842

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Algebraic Groups and Lie Groups with Few Factors by Alfonso Di Bartolo,Giovanni Falcone,Peter Plaumann,Karl Strambach Pdf

Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined.

Author : Anonim
Publisher : Unknown
Page : 780 pages
File Size : 48,7 Mb
Release : 1992-04-15
Category : Mathematics
ISBN : 9789814505918

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Collected Papers of Y Matsushima by Anonim Pdf

In the past thirty years, differential geometry has undergone an enormous change with infusion of topology, Lie theory, complex analysis, algebraic geometry and partial differential equations. Professor Matsushima played a leading role in this transformation by bringing new techniques of Lie groups and Lie algebras into the study of real and complex manifolds. This volume is a collection of all the 46 papers written by him. Contents:On Algebraic Lie Groups and AlgebrasOn a Theorem Concerning the Prolongation of a Differential SystemSome Studies on Kaehlerian Homogeneous SpacesOn the First Betti Number of Compact Quotient Spaces of Higher-Dimensional Symmetric SpacesOn the Cohomology Groups Attached to Certain Vector Valued Differential Forms on the Product of the Upper Half PlanesOn Certain Cohomology Groups Attached to Hermitian Symmetric SpacesHolomorphic Vector Fields and the First Chern Class of a Hodge ManifoldOn the Tube DomainsOn a Problem of Stoll Concerning a Cohomology Map from a Flag Manifold into a Grassmann ManifoldOn the Intermediate Cohomology Group of a Holomorphic Line Bundle over a Complex Torusand other papers Readership: Mathematicians. keywords:Matsushima;Differential Geometry;Topology;Lie Theory;Complex Analysis;Algebraic Geometry;Lie Groups;Lie Algebras;Real Manifolds;Complex Manifolds

Author : Deirdre Haskell,Anand Pillay,Charles Steinhorn
Publisher : Cambridge University Press
Page : 244 pages
File Size : 47,6 Mb
Release : 2000-07-03
Category : Mathematics
ISBN : 0521780683

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Model Theory, Algebra, and Geometry by Deirdre Haskell,Anand Pillay,Charles Steinhorn Pdf

Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.

Author : Michael Atiyah
Publisher : Unknown
Page : 400 pages
File Size : 45,9 Mb
Release : 1988-04-28
Category : Biography & Autobiography
ISBN : 019853275X

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Collected Works: Michael Atiyah Collected Works by Michael Atiyah Pdf

One of the greatest mathematicians in the world, Michael Atiyah has earned numerous honors, including a Fields Medal, the mathematical equivalent of the Nobel Prize. While the focus of his work has been in the areas of algebraic geometry and topology, he has also participated in research with theoretical physicists. For the first time, these volumes bring together Atiyah's collected papers--both monographs and collaborative works-- including those dealing with mathematical education and current topics of research such as K-theory and gauge theory. The volumes are organized thematically. They will be of great interest to research mathematicians, theoretical physicists, and graduate students in these areas.

Author : Rick Miranda
Publisher : American Mathematical Soc.
Page : 414 pages
File Size : 51,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821802687

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Algebraic Curves and Riemann Surfaces by Rick Miranda Pdf

In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.

Author : Yoz? Matsushima
Publisher : World Scientific
Page : 788 pages
File Size : 54,8 Mb
Release : 1992
Category : Mathematics
ISBN : 9810208146

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Collected Papers of Yoz“ Matsushima by Yoz? Matsushima Pdf

In the past thirty years, differential geometry has undergone an enormous change with infusion of topology, Lie theory, complex analysis, algebraic geometry and partial differential equations. Professor Matsushima played a leading role in this transformation by bringing new techniques of Lie groups and Lie algebras into the study of real and complex manifolds. This volume is a collection of all the 46 papers written by him.

Author : Donald Clayton Spencer
Publisher : World Scientific
Page : 694 pages
File Size : 55,7 Mb
Release : 1985
Category : Mathematics
ISBN : 9971978032

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Selecta by Donald Clayton Spencer Pdf

Author : Marc Hindry,Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 574 pages
File Size : 47,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461212102

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Diophantine Geometry by Marc Hindry,Joseph H. Silverman Pdf

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.

Author : Fred Diamond,Jerry Shurman
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 46,6 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387272269

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A First Course in Modular Forms by Fred Diamond,Jerry Shurman Pdf

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.