Description: Abelian Varieties over the Complex Numbers : A Graduate Course, Paperback by Lange, Herbert, ISBN 3031255690, ISBN-13 9783031255694, Like New Used, Free shipping in the US 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. Th 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. Th 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.
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Book Title: Abelian Varieties over the Complex Numbers : A Graduate Course
Number of Pages: Xii, 384 Pages
Language: English
Publication Name: Abelian Varieties over the Complex Numbers : a Graduate Course
Publisher: Springer International Publishing A&G
Subject: Geometry / General, General, Geometry / Algebraic, Complex Analysis
Publication Year: 2023
Type: Textbook
Item Weight: 21.3 Oz
Author: Herbert Lange
Subject Area: Mathematics
Item Length: 9.3 in
Series: Grundlehren Text Editions Ser.
Item Width: 6.1 in
Format: Trade Paperback
