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Item Details
Title: COMPLEX ABELIAN VARIETIES AND THETA FUNCTIONS
By: George R. Kempf
Format: Paperback

List price: £74.99


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ISBN 10: 3540531688
ISBN 13: 9783540531685
Publisher: SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG
Pub. date: 26 April, 1991
Edition: Softcover reprint of the original 1st ed. 1991
Series: Universitext
Pages: 105
Description: Focuses on analytical aspects of the geometry of abelian varieties, in order to provide an introduction to complex analytic geometry. The text features the systematic use of Mumford's theta group, which allows the author to provide precise results about the projective ideal of an abelian variety.
Synopsis: 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.
Illustrations: 1 Illustrations, black and white; IX, 105 p. 1 illus.
Publication: Germany
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Returns: Returnable
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