Moduli Of Curves And Abelian Varieties

Author : Carel Faber,Eduard Looijenga
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 48,7 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 : Carel Faber,Eduard Looijenga
Publisher : Unknown
Page : 212 pages
File Size : 46,6 Mb
Release : 1999-06-29
Category : Electronic
ISBN : 3322901734

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

Author : John Cremona,Joan-Carles Lario,Jordi Quer,Kenneth Ribet
Publisher : Birkhäuser
Page : 291 pages
File Size : 40,5 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 : Ke-Zheng Li,Frans Oort
Publisher : Springer
Page : 123 pages
File Size : 55,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540696667

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Moduli of Supersingular Abelian Varieties by Ke-Zheng Li,Frans Oort Pdf

Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool. For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. For low dimensions the moduli of supersingular abelian varieties is by now well understood. In this book we provide a description of the supersingular locus in all dimensions, in particular we compute the dimension of it: it turns out to be equal to Äg.g/4Ü, and we express the number of components as a class number, thus completing a long historical line where special cases were studied and general results were conjectured (Deuring, Hasse, Igusa, Oda-Oort, Katsura-Oort).

Author : Valery Alexeev,Arnaud Beauville,Charles Herbert Clemens,Elham Izadi
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 46,9 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 : Gerard van der Geer,C. Faber,Frans Oort
Publisher : Birkhäuser
Page : 526 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883030

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Moduli of Abelian Varieties by Gerard van der Geer,C. Faber,Frans Oort Pdf

Abelian varieties and their moduli are a topic of increasing importance in today`s mathematics, applications ranging from algebraic geometry and number theory to mathematical physics. This collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field.

Author : Ron Donagi
Publisher : American Mathematical Soc.
Page : 342 pages
File Size : 43,6 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 : Herbert Lange,Christina Birkenhake
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 42,7 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 : Olivier Debarre
Publisher : American Mathematical Soc.
Page : 124 pages
File Size : 54,7 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 : Klaus Hulek,Constantin Kahn,Steven H. Weintraub
Publisher : Walter de Gruyter
Page : 361 pages
File Size : 42,6 Mb
Release : 2011-05-03
Category : Mathematics
ISBN : 9783110891928

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Moduli Spaces of Abelian Surfaces by Klaus Hulek,Constantin Kahn,Steven H. Weintraub Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Author : Robert H. Dijkgraaf,Carel Faber,Gerard B.M. van der Geer
Publisher : Springer Science & Business Media
Page : 570 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242642

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The Moduli Space of Curves by Robert H. Dijkgraaf,Carel Faber,Gerard B.M. van der Geer Pdf

The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.

Author : Gerard van der Geer,C. Faber,Frans Oort
Publisher : Birkhäuser
Page : 518 pages
File Size : 48,8 Mb
Release : 2012-03-01
Category : Mathematics
ISBN : 3034883048

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Moduli of Abelian Varieties by Gerard van der Geer,C. Faber,Frans Oort Pdf

Abelian varieties and their moduli are a topic of increasing importance in today`s mathematics, applications ranging from algebraic geometry and number theory to mathematical physics. This collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field.

Author : Martin C. Olsson
Publisher : Springer
Page : 286 pages
File Size : 53,9 Mb
Release : 2008-07-25
Category : Mathematics
ISBN : 9783540705192

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Compactifying Moduli Spaces for Abelian Varieties by Martin C. Olsson Pdf

This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa.

Author : Gerd Faltings,Ching-Li Chai
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 55,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662026328

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Degeneration of Abelian Varieties by Gerd Faltings,Ching-Li Chai Pdf

A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.

Author : Herbert Lange
Publisher : Springer Nature
Page : 390 pages
File Size : 44,5 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.