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Complex Abelian Varieties

Author: Christina Birkenhake; Herbert Lange
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2004.
Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 302.
Edition/Format:   eBook : Document : English : Second, augmented editionView all editions and formats
Summary:
Abelian varieties are special examples of projective varieties. As such they can be described by a set of homogeneous polynomial equations. The theory of abelian 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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Christina Birkenhake; Herbert Lange
ISBN: 9783662063071 3662063077
OCLC Number: 851380558
Description: 1 online resource (xi, 638 pages).
Contents: Introduction --
Complex Tori --
Line Bundles on Complex Tori --
Cohomology of Line Bundles --
Abelian Varieties --
Endomorphisms of Abelian Varieties --
Theta and Heisenberg Groups --
Equations for Abelian Varieties --
Moduli --
Moduli Spaces of Abelian Varieties with Endomorphism Structure --
Abelian Surfaces --
Jacobian Varieties --
Prym Varieties --
Automorphisms --
Vector bundles on Abelian Varieties --
Further Results on Line Bundles an the Theta Divisor --
Cycles on Abelian Varieties --
The Hodge Conjecture for General Abelian and Jacobian Varieties --
Appendix: Algebraic Varieties and Complex Analytic Spaces --
Line Bundles and Factors of Automorphy --
Some Algebraic Geometric Results --
Derived Categories --
Moduli Spaces of Sheaves --
Abelian Schemes --
Index --
Glossary of Notation.
Series Title: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 302.
Responsibility: by Christina Birkenhake, Herbert Lange.

Abstract:

This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent  Read more...

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