Abelian Varieties, Theta Functions and the Fourier Transform (Cambridge Tracts in Mathematics #153) (Hardcover)

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Description


This book is 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. Alexander Polishchuk starts by discussing the classical theory of theta functions from the viewpoint 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 (originally due to Mumford) the Fourier-Mukai transform can often be used to simplify the existing proofs or to provide completely new proofs of many important theorems. This incisive volume is for graduate students and researchers with strong interest in algebraic geometry.
Product Details
ISBN: 9780521808040
ISBN-10: 0521808049
Publisher: Cambridge University Press
Publication Date: April 21st, 2003
Pages: 308
Language: English
Series: Cambridge Tracts in Mathematics