**AMS/IP Studies in Advanced Mathematics**

Volume: 10;
1999;
312 pp;
Hardcover

MSC: Primary 14;
Secondary 32; 81

Print ISBN: 978-0-8218-1193-1

Product Code: AMSIP/10

List Price: $53.00

Individual Member Price: $42.40

**Electronic ISBN: 978-1-4704-3801-2
Product Code: AMSIP/10.E**

List Price: $53.00

Individual Member Price: $42.40

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# Mirror Symmetry III

Share this page *Edited by *
*Duong H. Phong; Luc Vinet; Shing-Tung Yau*

A co-publication of the AMS and International Press of Boston, Inc.

This book presents surveys from a workshop held during the
theme year in geometry and topology at the Centre de recherches
mathématiques (CRM, University of Montréal). The volume
is in some sense a sequel to Mirror Symmetry
I (1998) and
Mirror Symmetry II (1996), copublished by the AMS and
International Press.

Included are recent developments in the theory of mirror manifolds
and the related areas of complex and symplectic geometry. The long
introductory articles explain the key physical ideas and motivation,
namely conformal field theory, supersymmetry, and string theory. Open
problems are emphasized. Thus the book provides an efficient way for a
very broad audience of mathematicians and physicists to reach the
frontier of research in this fast expanding area.

Features:

- Crucial research pertaining to future developments in algebraic and symplectic geometry and to the physics of unified string theories
- Well-known authors who are leaders in the field
- Introductory article by Greene and Yau
- A solid and even blend of ideas and techniques from both mathematics and physics

Also available from the AMS is the related volume, Mirror Symmetry IV (2002).

Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

#### Table of Contents

# Table of Contents

## Mirror Symmetry III

- Cover Cover11
- Title page v6
- Contents vii8
- Introduction ix10
- Aspects of quantum geometry 112
- Introduction to enumerative invariants 6980
- Compactified moduli spaces of pseudo-holomorphic curves 7788
- Mirror symmetry for hyper-Kähler manifolds 115126
- Connecting the web: A prognosis 157168
- Strong coupling singularities and non-abelian gauge symmetries in 𝑁=2 string theory 171182
- Remarks on (0,2) Calabi-Yau models 189200
- Relations among fixed point 197208
- An analytic discriminant for polarized algebraic 𝐾3 surfaces 211222
- Through the looking glass 263274
- An update on (small) quantum cohomology 279290
- Back Cover Back Cover1324

#### Readership

Graduate students, research mathematicians and physicists working in mathematics and theoretical physics, especially in algebraic or complex geometry or conformal field theory.