| 期刊全称 | Abelian Varieties over the Complex Numbers | | 期刊简称 | A Graduate Course | | 影响因子2023 | Herbert Lange | | 视频video | http://file.papertrans.cn/144/143135/143135.mp4 | | 发行地址 | Presents geometric constructions of the key abelian varieties: Jacobian, Albanese, Picard and Prym varieties.Introduces the Fourier–Mukai transform for sheaves and applies it to algebraic cycles and t | | 学科分类 | Grundlehren Text Editions | | 图书封面 |  | | 影响因子 | 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 al | | Pindex | Textbook 2023 |
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