Author | Birkenhake, Christina. author |
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Title | Complex Abelian Varieties [electronic resource] / by Christina Birkenhake, Herbert Lange |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004 |
Edition | Second, Augmented Edition |
Connect to | http://dx.doi.org/10.1007/978-3-662-06307-1 |
Descript | XI, 638 p. online resource |
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 Poincarยดe Bundle -- F.2 Relative Fourier Functor -- F.3 The Relative Jacobian -- Glossary of Notation