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Author: Ron Donagi
Publisher: American Mathematical Soc.
ISBN: 0821851438
Category : Mathematics
Languages : en
Pages : 354
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Book Description
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: Ron Donagi
Publisher: American Mathematical Soc.
ISBN: 0821851438
Category : Mathematics
Languages : en
Pages : 354
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Book Description
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
Publisher: Birkhäuser
ISBN: 3034879199
Category : Mathematics
Languages : en
Pages : 291
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Book Description
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: Werner Lütkebohmert
Publisher: Springer
ISBN: 331927371X
Category : Mathematics
Languages : en
Pages : 398
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Book Description
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: David Mumford
Publisher: Ann Arbor : University of Michigan Press, c1975, 1976 printing.
ISBN:
Category : Mathematics
Languages : en
Pages : 120
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Book Description
Author: Enrico Bombieri
Publisher: Cambridge University Press
ISBN: 9780521712293
Category : Mathematics
Languages : en
Pages : 676
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Book Description
This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.
Author: Valery Alexeev
Publisher: American Mathematical Soc.
ISBN: 0821843346
Category : Mathematics
Languages : en
Pages : 290
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Book Description
"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: Dan Abramovich
Publisher:
ISBN:
Category : Abelian varieties
Languages : en
Pages : 96
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Book Description
Author: David Mumford
Publisher: Ann Arbor : University of Michigan Press, c1975, 1976 printing.
ISBN:
Category : Mathematics
Languages : en
Pages : 120
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Book Description
Author: Herbert Lange
Publisher: Springer Science & Business Media
ISBN: 3662027887
Category : Mathematics
Languages : en
Pages : 443
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Book Description
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: Alexander Polishchuk
Publisher: Cambridge University Press
ISBN: 0521808049
Category : Mathematics
Languages : en
Pages : 308
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Book Description
Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
