Cover; Half-title; Title; Copyright; Contents; Preface; Acknowledgments; References; 1 Line Bundles on Complex Tori; 2 Representations of Heisenberg Groups I; 3 Theta Functions I; 4 Representations of Heisenberg Groups II: Intertwining Operators; 5 Theta Functions II: Functional Equation; 6 Mirror Symmetry for Tori; 7 Cohomology of a Line Bundle on a Complex Torus: Mirror Symmetry Approach; 8 Abelian Varieties and Theorem of the Cube; 9 Dual Abelian Variety; 10 Extensions, Biextensions, and Duality; 11 Fourier-Mukai Transform; 12 Mumford Group and Riemann's Quartic Theta Relation
Summary
The aim of this book is to present a modern treatment of the theory of theta functions in the context of algebraic geometry. The novelty of its approach lies in the systematic use of the Fourier-Mukai transform
Bibliography
Includes bibliographical references (pages 283-289) and index
