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Complex Abelian Varieties

  • Herbert Lange
  • Christina Birkenhake

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 302)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Herbert Lange, Christina Birkenhake
    Pages 1-4
  3. Herbert Lange, Christina Birkenhake
    Pages 5-5
  4. Herbert Lange, Christina Birkenhake
    Pages 6-22
  5. Herbert Lange, Christina Birkenhake
    Pages 23-45
  6. Herbert Lange, Christina Birkenhake
    Pages 46-70
  7. Herbert Lange, Christina Birkenhake
    Pages 71-114
  8. Herbert Lange, Christina Birkenhake
    Pages 115-146
  9. Herbert Lange, Christina Birkenhake
    Pages 147-181
  10. Herbert Lange, Christina Birkenhake
    Pages 182-211
  11. Herbert Lange, Christina Birkenhake
    Pages 212-246
  12. Herbert Lange, Christina Birkenhake
    Pages 247-287
  13. Herbert Lange, Christina Birkenhake
    Pages 288-319
  14. Herbert Lange, Christina Birkenhake
    Pages 320-364
  15. Herbert Lange, Christina Birkenhake
    Pages 365-408
  16. Back Matter
    Pages 409-435

About this book

Introduction

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.

Keywords

Abelian varieties Abelian variety Algebraic Curves Theta Function Theta Group algebra algebraic curve algebraic varieties cohomology field polynomial

Authors and affiliations

  • Herbert Lange
    • 1
  • Christina Birkenhake
    • 1
  1. 1.Mathematisches InstitutUniversität Erlangen-NürnbergErlangenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02788-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-02790-5
  • Online ISBN 978-3-662-02788-2
  • Series Print ISSN 0072-7830
  • Buy this book on publisher's site