Complex Abelian Varieties

Herbert Lange, Christina Birkenhake (auth.)3540204881, 9783540204886

May be used as an introduction or reference. Covers the theory of abelian varieties over the field of complex numbers. Topics include projective embeddings of an abelian variety including their equations and geometric properties, special results of Jacobians and Prym varieties allowing applications to the theory of algebraic curves, complex tori, cohomology of line bundles, and constructions of several moduli spaces of abelian varieties with additional structure. Problems follow each chapter.

---

Table of contents :
Front Matter….Pages i-viii
Introduction….Pages 1-4
Notation….Pages 5-5
Complex Tori….Pages 6-22
Line Bundles on Complex Tori….Pages 23-45
Cohomology of Line Bundles….Pages 46-70
Abelian Varieties….Pages 71-114
Endomorphisms of Abelian Varieties….Pages 115-146
Theta and Heisenberg Groups….Pages 147-181
Equations for Abelian Varieties….Pages 182-211
Moduli….Pages 212-246
Moduli Spaces of Abelian Varieties with Endomorphism Structure….Pages 247-287
Abelian Surfaces….Pages 288-319
Jacobian Varieties….Pages 320-364
Prym Varieties….Pages 365-408
Back Matter….Pages 409-435