Complex abelian varieties
Author(s)
Bibliographic Information
Complex abelian varieties
（Die Grundlehren der mathematischen Wissenschaften, 302）
Springer-Verlag, c1992
- : us
- : gw
Available at / 94 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: gwdc20:516.3/l262070244118
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Note
Includes bibliographical references (p. [417]-426) and index
Description and Table of Contents
Description
Abelian varieties are special examples of projective varieties. As such, they can be described by a set of homogeneous polynomial equations. The theory of Abelian varieties originated in the beginning of the 19th century with the work of Abel and Jacobi. The subject of this book is the theory of Abelian varieties over the field of complex numbers, and it covers the main results of the theory, both classic and recent, in modern language. It is intended to give a comprehensive introduction to the field, but also to serve as a reference. The focal topics are the projective embeddings of an Abelian variety, their equations and geometric properties. Moreover, several moduli spaces of Abelian varieties with additional structure are constructed. Some special results on Jacobians and Prym varieties allow applications to the theory of algebraic curves. The main tools for the proofs are the theta group of a line bundle, introduced by Mumford, and the characteristics to be associated to any nondegenerate line bundle. They are a direct generalization of the classical notion of characteristics of theta functions.
by "Nielsen BookData"