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Abelian Varieties, Theta Functions and the Fourier Transform

Abelian Varieties, Theta Functions and the Fourier Transform - 00 edition

Abelian Varieties, Theta Functions and the Fourier Transform - 00 edition

ISBN13: 9780511057588

ISBN10: 051105758X

Abelian Varieties, Theta Functions and the Fourier Transform by Polishchuk - ISBN 9780511057588
Edition: 00
Copyright: 2000
Publisher: Cambridge University Press
Published:
International: No
Abelian Varieties, Theta Functions and the Fourier Transform by Polishchuk - ISBN 9780511057588

ISBN13: 9780511057588

ISBN10: 051105758X

Edition: 00
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Summary

The aim of this book is to present a modern treatment of the theory of theta functions in the context of algebraic geometry. The novelty of its approach lies in the systematic use of the Fourier-Mukai transform. The author starts by discussing the classical theory of theta functions from the point of view of the representation theory of the Heisenberg group (in which the usual Fourier transform plays the prominent role). He then shows that in the algebraic approach to this theory, the Fourier-Mukai transform can often be used to simplify the existing proofs or to provide completely new proofs of many important theorems. Graduate students and researchers with strong interest in algebraic geometry will find much of interest in this volume.