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  3. Abelian Varieties, Theta Functions and the Fourier Transform
  • Cited by 61
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2009
      April 2003
      ISBN:
      9780511546532
      9780521808040
      DOI:
      https://doi.org/10.1017/CBO9780511546532
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.62kg, 308 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Geometry and Topology, Algebra
      Series:
      Cambridge Tracts in Mathematics (153)
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    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology, Algebra
    Series:
    Cambridge Tracts in Mathematics (153)
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    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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