Curves Jacobians And Abelian Varieties
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Curves Jacobians And Abelian Varieties
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Author : Ron Donagi
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Curves Jacobians And Abelian Varieties written by Ron Donagi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
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.
Curves And Abelian Varieties
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Author : Valery Alexeev
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Curves And Abelian Varieties written by Valery Alexeev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Abelian varieties categories.
"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.
Curves And Their Jacobians
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Author : David Mumford
language : en
Publisher: Ann Arbor : University of Michigan Press, c1975, 1976 printing.
Release Date : 1975
Curves And Their Jacobians written by David Mumford and has been published by Ann Arbor : University of Michigan Press, c1975, 1976 printing. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Rigid Geometry Of Curves And Their Jacobians
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Author : Werner Lütkebohmert
language : en
Publisher: Springer
Release Date : 2016-01-26
Rigid Geometry Of Curves And Their Jacobians written by Werner Lütkebohmert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-26 with Mathematics categories.
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.
Modular Curves And Abelian Varieties
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Author : John Cremona
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Modular Curves And Abelian Varieties written by John Cremona and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Abelian Varieties
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Author : S. Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-07
Abelian Varieties written by S. Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-07 with Mathematics categories.
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.
Decomposition Of Jacobians By Prym Varieties
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Author : Herbert Lange
language : en
Publisher: Springer Nature
Release Date : 2022-11-24
Decomposition Of Jacobians By Prym Varieties written by Herbert Lange and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-24 with Mathematics categories.
This monograph studies decompositions of the Jacobian of a smooth projective curve, induced by the action of a finite group, into a product of abelian subvarieties. The authors give a general theorem on how to decompose the Jacobian which works in many cases and apply it for several groups, as for groups of small order and some series of groups. In many cases, these components are given by Prym varieties of pairs of subcovers. As a consequence, new proofs are obtained for the classical bigonal and trigonal constructions which have the advantage to generalize to more general situations. Several isogenies between Prym varieties also result.
Abelian Varieties Over The Complex Numbers
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Author : Herbert Lange
language : en
Publisher: Springer Nature
Release Date : 2023-03-15
Abelian Varieties Over The Complex Numbers written by Herbert Lange and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-15 with Mathematics categories.
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.
Moduli Of Curves And Abelian Varieties
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Author : Carel Faber
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Moduli Of Curves And Abelian Varieties written by Carel Faber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
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.
Moduli Of Abelian Varieties
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Author : Allan Adler
language : en
Publisher: Springer
Release Date : 2006-11-14
Moduli Of Abelian Varieties written by Allan Adler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.