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9780821821275

Mirror Symmetry and Algebraic Geometry

by
  • ISBN13:

    9780821821275

  • ISBN10:

    082182127X

  • Format: Paperback
  • Copyright: 1999-09-01
  • Publisher: Amer Mathematical Society

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Summary

Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is the first completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, Kähler geometry, moduli of stable maps, Calabi-Yau manifolds, quantum cohomology, Gromov-Witten invariants, and the mirror theorem.

Table of Contents

Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
Hodge theory and Yukawa couplings
Moduli spaces Gromov-Witten invariants
Quantum cohomology Localization
Quantum differential equations
The mirror theorem Conclusion
Singular varieties
Physical theories
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

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