Mirror Symmetry / Edition 1

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Brand new. We distribute directly for the publisher. This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The ... first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry.The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the Calabi-Yau case. The book concludes with the first "naive" Givental computation, which is a mysterious mathematical justification of the computation of Candelas, et al. Read more Show Less

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Brand new. We distribute directly for the publisher. This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The ... first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry.The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the Calabi-Yau case. The book concludes with the first "naive" Givental computation, which is a mysterious mathematical justification of the computation of Candelas, et al. Read more Show Less

Ships from: Boonsboro, MD

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Overview

This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry. The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the Calabi-Yau case. The book concludes with the first ''naive'' Givental computation, which is a mysterious mathematical justification of the computation of Candelas, et al.

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Editorial Reviews

Booknews
Describes recent works motivated by the discovery of the mirror symmetry phenomenon by physicists. The book opens with the geometry of Calabi-Yau manifolds and the ideas from quantum field theory that led to this discovery. The rest of the book is devoted to the mathematical aspects of mirror symmetry. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780821819470
  • Publisher: American Mathematical Society
  • Publication date: 8/23/1999
  • Language: French
  • Series: Panoramas Et Synthaeses Series , #1
  • Edition number: 1
  • Pages: 120

Table of Contents

Introduction
Ch. 1 Calabi - Yau Manifolds 1
Ch. 2 "Physical" origin of the conjecture 21
Ch. 3 The Work of Candelas-de la Ossa - Green - Parkes 39
Ch. 4 The work of Batyrev 57
Ch. 5 Quantum cohomology 73
Ch. 6 The Givental Construction 95
Bibliography 117
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