Christina Birkenhake: Complex Abelian Varieties, Kartoniert / Broschiert

Klappentext

Notation.- 1. Complex Tori.- 2. Line Bundles on Complex Tori.- 3. Cohomology of Line Bundles.- 4. Abelian Varieties.- 5. Endomorphisms of Abelian Varieties.- 6. Theta and Heisenberg Groups.- 7. Equations for Abelian Varieties.- 8. Moduli.- 9. Moduli Spaces of Abelian Varieties with Endomorphism Structure.- 10. Abelian Surfaces.- 11. Jacobian Varieties.- 12. Prym Varieties.- 13. Automorphisms.- 14. Vector bundles on Abelian Varieties.- 15. Further Results on Line Bundles an the Theta Divisor.- 16. Cycles on Abelian varieties.- 17. The Hodge Conjecture for General Abelian and Jacobian Varieties.- A. Algebraic Varieties and Complex Analytic Spaces.- B. Line Bundles and Factors of Automorphy.- C. Some Algebraic Geometric Results.- C. 1 Some Properties of ?-Divisors.- C. 2 The Kodaira Dimension.- C. 3 Vanishing Theorems.- C. 6 Some Results from Intersection Theory.- C. 7 Adjoint Ideals.- D. Derived Categories.- D. 1 Definition and First Properties.- D. 2 Derived Functors.- D. 3 The Grothendieck-Riemann-Roch Theorem.- E. Moduli Spaces of Sheaves.- F. Abelian Schemes.- F. 1 Abelian Schemes and the Poincare Bundle.- F. 2 Relative Fourier Functor.- F. 3 The Relative Jacobian.- Glossary of Notation.