Curves Jacobians And Abelian Varieties

Author : Ron Donagi
Publisher : American Mathematical Soc.
Page : 342 pages
File Size : 50,9 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821851432

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Curves, Jacobians, and Abelian Varieties by Ron Donagi Pdf

This volume contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on the Schottky Problem, held in June 1990 at the University of Massachusetts at Amherst. The conference explored various aspects of the Schottky problem of characterizing Jacobians of curves among all abelian varieties. Some of the articles study related themes, including the moduli of stable vector bundles on a curve, Prym varieties and intermediate Jacobians, and special Jacobians with exotic polarizations or product structures.

Author : John Cremona,Joan-Carles Lario,Jordi Quer,Kenneth Ribet
Publisher : Birkhäuser
Page : 291 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879194

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Modular Curves and Abelian Varieties by John Cremona,Joan-Carles Lario,Jordi Quer,Kenneth Ribet Pdf

This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca Matemtica (Bellaterra, Barcelona). The articles in this volume present the latest achievements in this extremely active field and will be of interest both to specialists and to students and researchers. Many contributions focus on generalizations of the Shimura-Taniyama conjecture to varieties such as elliptic Q-curves and Abelian varieties of GL_2-type. The book also includes several key articles in the subject that do not correspond to conference lectures.

Author : Valery Alexeev,Arnaud Beauville,Charles Herbert Clemens,Elham Izadi
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 55,6 Mb
Release : 2008
Category : Abelian varieties
ISBN : 9780821843345

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Curves and Abelian Varieties by Valery Alexeev,Arnaud Beauville,Charles Herbert Clemens,Elham Izadi Pdf

"This book is devoted to recent progress in the study of curves and abelian varieties. It discusses both classical aspects of this deep and beautiful subject as well as two important new developments, tropical geometry and the theory of log schemes." "In addition to original research articles, this book contains three surveys devoted to singularities of theta divisors. of compactified Jucobiuns of singular curves, and of "strange duality" among moduli spaces of vector bundles on algebraic varieties."--BOOK JACKET.

Author : David Mumford
Publisher : Ann Arbor : University of Michigan Press, c1975, 1976 printing.
Page : 120 pages
File Size : 46,8 Mb
Release : 1975
Category : Mathematics
ISBN : UOM:39015061022490

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Curves and Their Jacobians by David Mumford Pdf

Author : David Mumford
Publisher : Ann Arbor : University of Michigan Press, c1975, 1976 printing.
Page : 120 pages
File Size : 50,7 Mb
Release : 1975
Category : Mathematics
ISBN : UOM:39015061022490

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Curves and Their Jacobians by David Mumford Pdf

Author : Jean-Pierre Serre
Publisher : CRC Press
Page : 203 pages
File Size : 47,7 Mb
Release : 1997-11-15
Category : Mathematics
ISBN : 9781439863862

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Abelian l-Adic Representations and Elliptic Curves by Jean-Pierre Serre Pdf

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 multiplication), where one

Author : S. Lang
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 54,7 Mb
Release : 2012-09-07
Category : Mathematics
ISBN : 9781441985347

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Abelian Varieties by S. Lang Pdf

It is with considerable pleasure that we have seen in recent years the simplifications expected by Weil realize themselves, and it has seemed timely to incorporate them into a new book. We treat exclusively abelian varieties, and have summarized in a first chapter all the general results on algebraic groups that are used in the sequel. We then deal with the Jacobian variety of a curve, the Albanese variety of an arbitrary variety, and its Picard variety, i.e., the theory of cycles of dimension 0 and co dimension 1. The numerical theory which gives the number of points of finite order on an abelian variety, and the properties of the trace of an endomorphism are simple formal consequences of the theory of the Picard variety and of numerical equivalence. The same thing holds for the Lefschetz fixed point formula for a curve, and hence for the Riemann hypothesis for curves. Roughly speaking, it can be said that the theory of the Albanese and Picard variety incorporates in purely algebraic terms the theory which in the classical case would be that of the first homology group.

Author : Werner Lütkebohmert
Publisher : Springer
Page : 386 pages
File Size : 53,8 Mb
Release : 2016-01-26
Category : Mathematics
ISBN : 9783319273716

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Rigid Geometry of Curves and Their Jacobians by Werner Lütkebohmert Pdf

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 varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.

Author : Enrico Bombieri,Walter Gubler
Publisher : Cambridge University Press
Page : 676 pages
File Size : 49,6 Mb
Release : 2006
Category : Mathematics
ISBN : 0521712297

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Heights in Diophantine Geometry by Enrico Bombieri,Walter Gubler Pdf

This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.

Author : Alexander Polishchuk
Publisher : Cambridge University Press
Page : 308 pages
File Size : 43,9 Mb
Release : 2003-04-21
Category : Mathematics
ISBN : 9780521808040

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Abelian Varieties, Theta Functions and the Fourier Transform by Alexander Polishchuk Pdf

Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.

Author : Herbert Lange,Christina Birkenhake
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 50,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662027882

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Complex Abelian Varieties by Herbert Lange,Christina Birkenhake Pdf

Abelian varieties are special examples of projective varieties. As such theycan be described by a set of homogeneous polynomial equations. The theory ofabelian varieties originated in the beginning of the ninetheenth centrury with the work of Abel and Jacobi. The subject of this book is the theory of abelian varieties over the field of complex numbers, and it covers the main results of the theory, both classic and recent, in modern language. It is intended to give a comprehensive introduction to the field, but also to serve as a reference. The focal topics are the projective embeddings of an abelian variety, their equations and geometric properties. Moreover several moduli spaces of abelian varieties with additional structure are constructed. Some special results onJacobians and Prym varieties allow applications to the theory of algebraic curves. The main tools for the proofs are the theta group of a line bundle, introduced by Mumford, and the characteristics, to be associated to any nondegenerate line bundle. They are a direct generalization of the classical notion of characteristics of theta functions.

Author : Allan Adler,Sundararaman Ramanan
Publisher : Springer
Page : 205 pages
File Size : 45,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540496090

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Moduli of Abelian Varieties by Allan Adler,Sundararaman Ramanan Pdf

This is a book aimed at researchers and advanced graduate students in algebraic geometry, interested in learning about a promising direction of research in algebraic geometry. It begins with a generalization of parts of Mumford's theory of the equations defining abelian varieties and moduli spaces. It shows through striking examples how one can use these apparently intractable systems of equations to obtain satisfying insights into the geometry and arithmetic of these varieties. It also introduces the reader to some aspects of the research of the first author into representation theory and invariant theory and their applications to these geometrical questions.

Author : G. Cornell,J. H. Silverman
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461386551

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Arithmetic Geometry by G. Cornell,J. H. Silverman Pdf

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 expository lectures, this volume contains a translation into English of Falt ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation.

Author : Carel Faber,Eduard Looijenga
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783322901729

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Moduli of Curves and Abelian Varieties by Carel Faber,Eduard Looijenga Pdf

The Dutch Intercity Seminar on Moduli, which dates back to the early eighties, was an initiative of G. van der Geer, F. Oort and C. Peters. Through the years it became a focal point of Dutch mathematics and it gained some fame, also outside Holland, as an active biweekly research seminar. The tradition continues up to today. The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Hain, E. Looijenga, and F. Oort, originates from the seminar held in 1995--96. Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles.

Author : Herbert Lange
Publisher : Springer Nature
Page : 390 pages
File Size : 46,9 Mb
Release : 2023-03-15
Category : Mathematics
ISBN : 9783031255700

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Abelian Varieties over the Complex Numbers by Herbert Lange Pdf

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 with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier–Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained. This book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.