Overview
- Authors:
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Herbert Lange
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Mathematisches Institut, Universität Erlangen-Nürnberg, Erlangen, Germany
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Christina Birkenhake
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Mathematisches Institut, Universität Erlangen-Nürnberg, Erlangen, Germany
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Table of contents (14 chapters)
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Front Matter
Pages i-viii
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- Herbert Lange, Christina Birkenhake
Pages 1-4
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- Herbert Lange, Christina Birkenhake
Pages 5-5
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- Herbert Lange, Christina Birkenhake
Pages 6-22
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- Herbert Lange, Christina Birkenhake
Pages 23-45
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- Herbert Lange, Christina Birkenhake
Pages 46-70
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- Herbert Lange, Christina Birkenhake
Pages 71-114
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- Herbert Lange, Christina Birkenhake
Pages 115-146
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- Herbert Lange, Christina Birkenhake
Pages 147-181
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- Herbert Lange, Christina Birkenhake
Pages 182-211
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- Herbert Lange, Christina Birkenhake
Pages 212-246
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- Herbert Lange, Christina Birkenhake
Pages 247-287
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- Herbert Lange, Christina Birkenhake
Pages 288-319
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- Herbert Lange, Christina Birkenhake
Pages 320-364
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- Herbert Lange, Christina Birkenhake
Pages 365-408
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Back Matter
Pages 409-435
About this book
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.
Reviews
"This beautiful book is a very important and valuable contribution to the literature...it contains a wealth of material which so far is only available in the original papers and as such the book is also of great value for the experts. It is a book which truly belongs to the series Grundlehren der mathematischen Wissenschaft!" - Mededelingen van het wiskundig genootschap
