Buch, Englisch, Band 302, 638 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 972 g
Buch, Englisch, Band 302, 638 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 972 g
Reihe: Grundlehren der mathematischen Wissenschaften
ISBN: 978-3-642-05807-3
Verlag: Springer
This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture. ". far more readable than most. it is also much more complete." Olivier Debarre in Mathematical Reviews, 1994.
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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 Poincar´e Bundle.- F.2 Relative Fourier Functor.- F.3 The Relative Jacobian.- Glossary of Notation.
