Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms (Lecture Notes in Mathematics (1845))

This volume deals with various topics around equivariant holomorphic maps of Hermitian symmetric domains and is intended for specialists in number theory and algebraic geometry. In particular, it contains a comprehensive exposition of mixed automorphic forms that has never yet appeared in book form. The main goal is to explore connections among complex torus bundles, mixed automorphic forms, and Jacobi forms associated to an equivariant holomorphic map. Both number-theoretic and algebro-geometric aspects of such connections and related topics are discussed. This volumedeals with various topicsaround equivariant holomorphic maps of Hermitian symmetric domains and is intended for specialists in number theory and algebraic geometry. In particular, it contains a comprehensive exposition of mixed automorphic forms that has never yetappeared in book form. The main goalis to explore connections among complex torus bundles, mixed automorphic forms, and Jacobi forms associated to an equivariant holomorphic map. Both number-theoretic and algebro-geometric aspects of such connections and related topics are discussed. TOC:Introduction.- 1. Mixed Automorphic Forms.- 2. Line Bundles and Elliptic Varieties.- 3. Mixed Automorphic Forms and Cohomology.- 4. Mixed Hilbert and Siegel Modular Forms.- 5. Mixed Automorphic Forms on Semisimple Lie Groups.- 6. Families of Abelian Varieties.- 7. Jacobi Forms.- 8. Twisted Torus Bundles.- References.- Index Introduction....Pages 1-9 1. Mixed Automorphic Forms....Pages 11-34 2. Line Bundles and Elliptic Varieties....Pages 35-58 3. Mixed Automorphic Forms and Cohomology....Pages 59-82 4. Mixed Hilbert and Siegel Modular Forms....Pages 83-107 5. Mixed Automorphic Forms on Semisimple Lie Groups....Pages 109-139 6. Families of Abelian Varieties....Pages 141-175 7. Jacobi Forms....Pages 177-207 8. Twisted Torus Bundles....Pages 209-230 References....Pages 231-236