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  3. Abelian Varieties, Theta Functions and the Fourier Transform
  • Cited by 59
Publisher:
Cambridge University Press
Online publication date:
August 2009
Print publication year:
2003
Online ISBN:
9780511546532
DOI:
https://doi.org/10.1017/CBO9780511546532
Subjects:
Mathematics (general), Mathematics, Geometry and Topology, Algebra
Series:
Cambridge Tracts in Mathematics (153)
Information

Book description

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.

Reviews

'The book is written by a leading expert in the field and it will certainly be a valuable enhancement to the existing literature.'

Source: EMS Newsletter

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