ENGLISH

Complex Abelian Varieties and Theta Functions

By George R. Kempf

Book information

Publisher
Springer
Year
1991
ISBN
0387531688, 9780387531687
LCC
QA564 .K45 1991
Language
english
Format
PDF
Filesize
3 MB (3110060 bytes)
Series
Universitext
Edition
First Edition
Pages
96\104
Time added
2011-06-04 13:46:07

Description

Abelian varieties are a natural generalization of elliptic curves to higher dimensions, whose geometry and classification are as rich in elegant results as in the one-dimensional ease. The use of theta functions, particularly since Mumford's work, has been an important tool in the study of abelian varieties and invertible sheaves on them. Also, abelian varieties play a significant role in the geometric approach to modern algebraic number theory. In this book, Kempf has focused on the analytic aspects of the geometry of abelian varieties, rather than taking the alternative algebraic or arithmetic points of view. His purpose is to provide an introduction to complex analytic geometry. Thus, he uses Hermitian geometry as much as possible. One distinguishing feature of Kempf's presentation is the systematic use of Mumford's theta group. This allows him to give precise results about the projective ideal of an abelian variety. In its detailed discussion of the cohomology of invertible sheaves, the book incorporates material previously found only in research articles. Also, several examples where abelian varieties arise in various branches of geometry are given as a conclusion of the book.

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