**AMS/IP Studies in Advanced Mathematics**

Volume: 9;
1998;
444 pp;
Softcover

MSC: Primary 14;
Secondary 32; 81

Print ISBN: 978-0-8218-2743-7

Product Code: AMSIP/9.S

List Price: $63.00

Individual Member Price: $50.40

**Electronic ISBN: 978-1-4704-3800-5
Product Code: AMSIP/9.E**

List Price: $63.00

Individual Member Price: $50.40

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# Mirror Symmetry I

Share this page *Edited by *
*Shing-Tung Yau*

#### Readership

Graduate students, research mathematicians and mathematical physicists working in algebraic geometry, mathematical physics, and number theory.

#### Reviews & Endorsements

This volume is very timely, giving very broad coverage of one of the important developments in mathematics and physics today … This volume is a requisite for those working in the area of CY \(3\)-folds, as well as those interested in mathematical implications of contemporary physics.

-- Mathematical Reviews

# Table of Contents

## Mirror Symmetry I

- Cover Cover11
- Title page v6
- Contents vii8
- Preface to the new edition ix10
- Introduction xi12
- An introduction to mirror manifolds 116
- A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory 3146
- Topological mirrors and quantum rings 97112
- Mirror manifolds and topological field theory 121136
- Rational curves and classification of algebraic varieties 161176
- Rational curves on Calabi-Yau threefolds 169184
- Picard-Fuchs equations and mirror maps for hypersurfaces 185200
- Kähler classes on Calabi-Yau threefolds—An informal survey 201216
- Automorphic functions and special Kähler geometry 215230
- Picard-Fuchs equations and flat holomorphic connections from 𝑁=2 supergravity 237252
- A new geometry from superstring theory 253268
- The geometry of Calabi-Yau orbifolds 279294
- Properties of superstring vacua from (topological) Landau-Ginzburg models 287302
- An 𝑆𝐿(2,ℂ) action on certain Jacobian rings and the mirror map 311326
- A generalized construction of mirror manifolds 327342
- New constructions of mirror manifolds: Probing moduli space far from Fermat points 347362
- Deformations of Calabi-Yau Kleinfolds 391406
- Smoothing 3-folds with trivial canonical bundle and ordinary double points 399414
- Modified Calabi-Yau manifolds with torsion 421436
- Calabi-Yau threefolds and complex multiplication 431446
- Back Cover Back Cover1460