Abelian Varieties Over The Complex Numbers A Graduate Course 1st Edition Herbert Lange by Herbert Lange 9783031255694, 9783031255700, 9783031444463, 3031255690, 3031255704, 3031444469 instant download after payment.

Mathematics Subject Classification (2020): • 14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry • 14Kxx Abelian varieties and schemes • 14D20 Algebraic moduli problems, moduli of vector bundles • 14H40 Jacobians, Prym varieties • 14H42 Theta functions and curves; Schottky problem

This textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles.

The book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. 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. 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.

This book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.