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Mirror Symmetry I

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Brand new. We distribute directly for the publisher. This volume is an updated edition of Essays on Mirror Manifolds, the first book of papers published after the phenomenon of ... mirror symmetry was discovered. The two major groups who made the discovery reported their papers here.Greene, Plesser, and Candelas gave details on their findings; Witten gave his interpretation which was vital for future development. Vafa introduced the concept of quantum cohomology. Several mathematicians, including Katz, Morrison, Wilson, Roan, Tian, Hbsch, Yau, and Borcea discussed current knowledge about Calabi-Yau manifolds. Ferrara and his coauthors addressed special geometry and $N=2$ supergravity. Roček proposed possible mirrors for Calabi-Yau manifolds with torsion. This collection continues to be an important book on this spectacular achievement in algebraic geometry and mathematical physics. Read more Show Less

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Overview

This volume is an updated edition of Essays on Mirror Manifolds, the first book of papers published after the phenomenon of mirror symmetry was discovered. The two major groups who made the discovery reported their papers here. Greene, Plesser, and Candelas gave details on their findings; Witten gave his interpretation which was vital for future development. Vafa introduced the concept of quantum cohomology. Several mathematicians, including Katz, Morrison, Wilson, Roan, Tian, Hubsch, Yau, and Borcea discussed current knowledge about Calabi-Yau manifolds. Ferrara and his coauthors addressed special geometry and $N=2$ supergravity. Rocek proposed possible mirrors for Calabi-Yau manifolds with torsion. This collection continues to be an important book on this spectacular achievement in algebraic geometry and mathematical physics. Also available from the AMS are the related volumes, Mirror Symmetry II (1996), Mirror Symmetry III (1999), and Mirror Symmetry IV (2002).

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Editorial Reviews

Booknews
A collection of papers from a 1991 workshop on mirror manifolds at the Mathematical Sciences Research Institute, originally published as Essays on Mirror Manifolds. Subjects include mirror manifolds and topological field theory, rational curves and classification of algebraic varieties, Picard-Fuchs equations and mirror maps for hypersurfaces, a new geometry from superstring theory, and deformations of Calabi-Yau Kleinfolds. This edition is supplemented by an additional volume, Mirror Symmetry 2. For graduate students, research mathematicians, and mathematical physicists working in algebraic geometry, mathematical physics, and number theory. No index. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

Table of Contents

Preface
Introduction
An introduction to mirror manifolds 1
A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory 31
Topological mirrors and quantum rings 97
Mirror manifolds and topological field theory 121
Rational curves and classification of algebraic varieties 161
Rational curves on Calabi-Yau threefolds 169
Picard-Fuchs equations and mirror maps for hypersurfaces 185
Kahler classes on Calabi-Yau threefolds - An informal survey 201
Automorphic functions and special Kahler geometry 215
Picard-Fuchs equations and flat holomorphic connections from N = 2 supergravity 237
A new geometry from superstring theory 253
The geometry of Calabi-Yau orbifolds 279
Properties of superstring vacua from topological Landau-Ginzburg models 287
An SL2,C action on certain Jacobian rings and the mirror map 311
A generalized construction of mirror manifolds 327
New constructions of mirror manifolds: Probing moduli space far from Fermat points 347
Deformations of Calabi-Yau Kleinfolds 391
Smoothing 3-folds with trivial canonical bundle and ordinary double points 399
Modified Calabi-Yau manifolds with torsion 421
Calabi-Yau threefolds and complex multiplication 431
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