Subsequently, the Fourier–Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles.
This textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry.
