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Abelian varieties, theta functions, and the Fourier transform / Alexander Polishchuk.

By: Material type: TextTextSeries: Cambridge tracts in mathematics ; 153.Publication details: Cambridge, UK ; New York : Cambridge University Press, 2003.Description: 1 online resource (xvi, 292 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 0511063911
  • 9780511063916
  • 0511072376
  • 9780511072376
  • 9780511546532
  • 051154653X
  • 9780521808040
  • 0521808049
Subject(s): Genre/Form: Additional physical formats: Print version:: Abelian varieties, theta functions, and the Fourier transform.DDC classification:
  • 516.3/5 22
LOC classification:
  • QA564 .P64 2003eb
Online resources:
Contents:
Cover; Half-title; Title; Copyright; Contents; Preface; Acknowledgments; References; 1 Line Bundles on Complex Tori; 2 Representations of Heisenberg Groups I; 3 Theta Functions I; 4 Representations of Heisenberg Groups II: Intertwining Operators; 5 Theta Functions II: Functional Equation; 6 Mirror Symmetry for Tori; 7 Cohomology of a Line Bundle on a Complex Torus: Mirror Symmetry Approach; 8 Abelian Varieties and Theorem of the Cube; 9 Dual Abelian Variety; 10 Extensions, Biextensions, and Duality; 11 Fourier-Mukai Transform; 12 Mumford Group and Riemann's Quartic Theta Relation.
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.
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library EBSCO Mathematics Available
Total holds: 0

Includes bibliographical references (pages 283-289) and index.

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.

Cover; Half-title; Title; Copyright; Contents; Preface; Acknowledgments; References; 1 Line Bundles on Complex Tori; 2 Representations of Heisenberg Groups I; 3 Theta Functions I; 4 Representations of Heisenberg Groups II: Intertwining Operators; 5 Theta Functions II: Functional Equation; 6 Mirror Symmetry for Tori; 7 Cohomology of a Line Bundle on a Complex Torus: Mirror Symmetry Approach; 8 Abelian Varieties and Theorem of the Cube; 9 Dual Abelian Variety; 10 Extensions, Biextensions, and Duality; 11 Fourier-Mukai Transform; 12 Mumford Group and Riemann's Quartic Theta Relation.

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