TY  - BOOK
AU  - Christina Birkenhake
AU  -  Herbert Lange
TI  - Complex Abelian varieties: : second edition
T2  - Grundlehren der mathematischen Wissenschaften 
SN  - 9783540204886
AV  - QA564 
PY  - 1980///]
CY  - Heidelberg
PB  - Springer-Verlag
KW  - Mathematics
N1  - 1. Introduction
2. Notation
3. Complex Tori
4. Line Bundles on Complex Tori
5. Cohomology of Line Bundles
6. Abelian Varieties
7. Endomorphisms of Abelian Varieties
8. Theta and Heisenberg Groups
9. Equations for Abelian Varieties
10. Moduli
11. Moduli Spaces of Abelian Varieties with Endomorphism Structure
12. Abelian Surfaces
13. Jacobian Varieties
14. Prym Varieties
15. Automorphisms
16. Vector bundles on Abelian Varieties
17. Further Results on Line Bundles an the Theta Divisor
18. Cycles on Abelian varieties
19. The Hodge Conjecture for General Abelian and Jacobian Varieties
N2  - 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 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. --- summary provided by publisher
ER  -