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Abelian Varieties over the Complex Numbers

Name: Abelian Varieties over the Complex Numbers
Brand: Springer, Berlin
SKU: 9783031255694
Price: 1231 CZK
Availability: InStock

A Graduate Course

Autor: Herbert Lange

Jazyk:

Vazba: Brožovaná

Vydavatel: Springer, Berlin

Dostupnost: Skladem u dodavatele

Odesíláme za 5-8 dnů

1 231 Kč

This textbook offers an introduction to abelian varieties, a rich topic of central importance to alg...

Informace o knize

Autor

Herbert Lange

Jazyk

Angličtina

Vazba

Kniha - Brožovaná

Vydáno

2023

Stránek

384

EAN

9783031255694

Enbook ID

42567893

Vydavatel

Springer, Berlin

Hmotnost

610

Rozměry

155 x 235

Kompletní popis

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.