Mirror Symmetry III: Proceedings of the Conference on Complex Geometry and Mirror Symmetry, Montreal, 1995

324 Pages·1998·37.94 MB·English

by  Duong H. Phong (editor), Luc Vinet (editor), Shing-Tung Yau (editor)

Selected Title s i n This Serie s
Volume
10 Duon g H. Phong, Lu c Vinet, and Shing-Tung Yau , Editor s
Mirror Symmetry III
1999
9 Shing-Tun g Yau, Edito r
Mirror Symmetry I
1998
8 Jiirge n Jost, Wilfrid Kendall, Umberto Mosco , Michael Rockner ,
and Karl-Theodor Stur m
New Directions in Dirichlet Forms
1998
7 D . A. Buell and J. T. Teitelbaum, Editor s
Computational Perspectives on Number Theor y
1998
6 Harol d Levin e
Partial Differential Equation s
1997
5 Qi-ken g Lu, Stephen S.-T. Yau, and Anatoly Libgober , Editor s
Singularities and Complex Geometry
1997
4 Vyjayanth i Char i and Ivan B, Penkov, Editor s
Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras
1997
3 Xia-X i Din g and Tai-Ping Liu, Editor s
Nonlinear Evolutionary Partial Differential Equation s
1997
2.2 Willia m H. Kazez, Edito r
Geometric Topology
1997
2.1 Willia m H. Kazez, Edito r
Geometric Topology
1997
1 B . Green e and S.-T. Yau, Editor s
Mirror Symmetry II
1997
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Mirror
Symmetry III
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https://doi.org/10.1090/amsip/010
AMS/IP
Studies in
Advanced
Mathematics
Volume 10
Mirror
Symmetry III
Proceedings of the Conference
on Complex Geometry and
Mirror Symmetry, Montreal, 1995
Duong H. Phong, Luc Vinet, and
Shing-Tung Yau, Editors
America n Centr e de
Internationa l
Mathematica l Recherche s
Pres s
Society Mathematique s
Shing-Tung Yau, Managing Edito r
1991 Mathematics Subject Classification. Primar y 14-06 ; Secondary 32-06, 81-06.
Library of Congress Cataloging-in-Publication Dat a
Conference on Complex Geometry and Mirror Symmetry (1995 : Montreal, Quebec)
Mirror symmetr y II I : proceedings o f the Conferenc e o n Comple x Geometr y an d Mirro r
Symmetry, Montreal, 1995 / Duong H. Phong, Luc Vinet, and Shing-Tung Yau, editors,
p. cm. — (AMS/IP studies in advanced mathematics ; v. 10)
Includes bibliographical references.
ISBN 0-8218-1193-2
1. Mirror symmetry—Congresses . 2 . Geometry, Differential—Congresses . 3 . Functions of
several complex variables—Congresses. I . Phong, Duong H., 1953- . II . Vinet, Luc. III . Yau,
Shing-Tung, 1949- . IV . Title. V . Title: Mirror symmetry three. VI . Series.
QC174.17.S9C63 199 5
516.3/62—dc21 98-3764 3
CIP
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© 199 9 by the American Mathematical Society, International Press and the Centre de
Recherches Mathematiques. All rights reserved.
The American Mathematical Society, International Press and the Centre de
Recherches Mathematiques retain all rights
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10 9 8 7 6 5 4 3 2 1 0 4 03 02 01 00 99
Contents
Introduction
Aspects of Quantum Geometry
Brian R. Greene
Introduction to Enumerative Invariants
Shing-Tung Yau
Compactified Moduli Spaces of Pseudo-Holomorphic Curves
Thomas H. Parker
Mirror Symmetry for Hyper-Kahler Manifold s
Misha Verbitsky
Connecting the Web: A Prognosis
Mark Gross
Strong Coupling Singularities and Non-Abelian Gauge Symmetries in
String Theory
Albrecht Klemm and Peter Mayr
Remarks on (0,2) Calabi-Yau Models
Shamit Kachru
Relations Among Fixed Point
Kefeng Liu
An Analytic Discriminant for Polarized Algebraic K3 Surface s
Jay Jorgenson and Andrey Todorov
Through the Looking Glass
David R. Morrison
An Update on (Small) Quantum Cohomology
Bernd Siebert
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Introduction
This book has its origin in a workshop on Complex Geometry and Mirror Sym-
metry held in the framework of a theme year program in Geometry and Topology
at the Centre de recherches mathematiques (CRM), Universite de Montreal, in the
spring 1995. It is published thanks to an Agreement between the American Math-
ematical Society, the CRM, and International Press and is in some sense a sequel
to "Mirro r Symmetr y I " an d "Mirro r Symmetr y II" publishe d b y the America n
Mathematical Society and International Press.
During the workshop, physicists and mathematicians actively discussed ques-
tions related to the development o f string theory. Bria n Greene gave a beautifu l
overview of the subject. Topic s on enumerative geometry, vector bundles in super
Calabi-Yau manifolds, localizatio n techniques, and analytic invariants associate d
to K3 surfac e are covered in this collection of papers.
We are grateful to the CRM for hosting such a fruitful meeting .
The Editors
IX