Abelian Varieties over the Complex Numbers: A Graduate Course - Couverture rigide

Lange, Herbert

Couverture rigide

ISBN 10 : 3031444469 ISBN 13 : 9783031444463

Editeur : Springer International Publishing AG, 2024

Synopsis

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.

A propos du livre

À propos de l'auteur

Herbert Lange, now retired, was a professor at the department of mathematics of the University Erlangen-Nuremberg. He has published more than 130 research papers on abelian varieties, curve theory and vector bundles on algebraic curves, as well as several books.

Détails de l'édition

• Éditeur: Springer International Publishing AG
• Date d'édition: 2024
• Langue: anglais
• ISBN 10: 3031444469
• ISBN 13: 9783031444463
• Reliure: Relié
• Nombre de pages: 396
• Coordonnées du fabricant: GPSR Kontakt; ProductSafety@springernature.com; ; Tiergartenstr. 17; Heidelberg; 69121; Allemagne