Abelian Varieties Over the Complex Numbers is popular PDF and ePub book, written by Herbert Lange in 2023, it is a fantastic choice for those who relish reading online the Uncategoriezed genre. Let's immerse ourselves in this engaging Uncategoriezed book by exploring the summary and details provided below. Remember, Abelian Varieties Over the Complex Numbers can be Read Online from any device for your convenience.
Abelian Varieties Over the Complex Numbers Book PDF Summary
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.
Detail Book of Abelian Varieties Over the Complex Numbers PDF
- Author : Herbert Lange
- Release : 02 July 2024
- Publisher : Unknown
- ISBN : 3031255712
- Genre : Uncategoriezed
- Total Page : 0 pages
- Language : English
- PDF File Size : 21,9 Mb
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