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Moduli of Abelian Varieties

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 03X/5 ( reviews)

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Book Synopsis Moduli of Abelian Varieties by : Gerard van der Geer

Download or read book Moduli of Abelian Varieties written by Gerard van der Geer. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Moduli of Supersingular Abelian Varieties

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 660/5 ( reviews)

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Book Synopsis Moduli of Supersingular Abelian Varieties by : Ke-Zheng Li

Download or read book Moduli of Supersingular Abelian Varieties written by Ke-Zheng Li. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Compactifying Moduli Spaces for Abelian Varieties

2008-08-25 Mathematics
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Release : 2008-08-25
Genre : Mathematics
Kind : eBook
Book Rating : 18X/5 ( reviews)

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Book Synopsis Compactifying Moduli Spaces for Abelian Varieties by : Martin C. Olsson

Download or read book Compactifying Moduli Spaces for Abelian Varieties written by Martin C. Olsson. This book was released on 2008-08-25. Available in PDF, EPUB and Kindle. Book excerpt: 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. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.

Degeneration of Abelian Varieties

2013-04-17 Mathematics
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Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 325/5 ( reviews)

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Book Synopsis Degeneration of Abelian Varieties by : Gerd Faltings

Download or read book Degeneration of Abelian Varieties written by Gerd Faltings. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Complex Abelian Varieties

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 887/5 ( reviews)

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Book Synopsis Complex Abelian Varieties by : Herbert Lange

Download or read book Complex Abelian Varieties written by Herbert Lange. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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