AMS/IP Studies in Advanced Mathematics 1996; 844 pp; softcover Volume: 1 Reprint/Revision History: reprinted 2001 ISBN10: 0821827448 ISBN13: 9780821827444 List Price: US$109 Member Price: US$87.20 Order Code: AMSIP/1.S
 Mirror symmetry has undergone dramatic progress during the last five years. Tremendous insight has been gained on a number of key issues. This volume surveys these results. Some of the contributions in this work have appeared elsewhere, while others were written specifically for this collection. The areas covered are organized into 4 sections, and each presents papers by both physicists and mathematicians. This volume collects the most important developments that have taken place in mathematical physics since 1991. It is an essential reference tool for both mathematics and physics libraries and for students of physics and mathematics. Also available from the AMS are the related volumes, Mirror Symmetry I (1998), Mirror Symmetry III (1999), and Mirror Symmetry IV (2002). Titles in this series are copublished with International Press of Boston, Inc., Cambridge, MA. Readership Graduate students, research mathematicians, and physicists interested in mathematical physics. Reviews "The papers of this volume will undoubtedly allow the reader to gain much insight into both the physics and the mathematics of the remarkable structure of mirror symmetry."  Zentralblatt MATH Table of Contents Construction of mirror manifolds  B. R. Greene and H. Ooguri  Geometry and quantum field theory: A brief introduction
 R. R. Greene  Constructing mirror manifolds
 V. V. Batyrev and L. A. Borisov  Dual cones and mirror symmetry
 P. Berglund and S. Katz  Mirror symmetry constructions: A review
 P. Berglund and M. Henningson  On the elliptic genus and mirror symmetry
 S.s. Roan  Orbifold Euler characteristic
The structure of moduli space  E. Witten  Phases of \(N=2\) theories in two dimensions
 P. S. Aspinwall, B. R. Greene, and D. R. Morrison  CalabiYau moduli space, mirror manifolds and spacetime topology change in string theory
 A. Ceresole, R. D'Auria, S. Ferrara, W. Lerche, J. Louis, and T. Regge  PicardFuchs equations, special geometry and target space duality
 P. S. Aspinwall  Resolution of orbifold singularities in string theory
 P. H. Wilson  The role of \(c_2\) in CalabiYau classificationa preliminary survey
 Z. Ran  Thickening CalabiYau moduli spaces
 M. Gross  The deformation space of CalabiYau \(n\)folds with canonical singularities can be obstructed
 A. Giveon and M. Roček  Introduction to duality
 E. Kiritsis, C. Kounnas, and D. Lüst  Noncompact CalabiYau spaces and other nontrivial backgrounds for fourdimensional superstrings
 R. Schimmrigk  Scaling behavior on the space of CalabiYau manifolds
Enumerative issues and mirror symmetry  D. R. Morrison  Making enumerative predictions by means of mirror symmetry
 P. Candelas, X. l. Ossa, A. Font, S. Katz, and D. R. Morrison  Mirror symmetry for two parameter modelsI
 S. Hosono, A. Klemm, S. Theisen, and S.T. Yau  Mirror symmetry, mirror map and applications to complete intersection CalabiYau spaces
 M. Kontsevich and Yu. Manin  GromovWitten classes, quantum cohomology, and enumerative geometry
 M. Bershadsky, S. Cecotti, H. Ooguri, and C. Vafa  Holomorphic anomalies in topological field theories
 P. Deligne  Local behavior of Hodge structures at infinity
Mirror symmetry in higher and lower dimensions  P. S. Aspinwall and D. R. Morrison  String theory on K3 surfaces
 C. Borcea  K3 surfaces with involution and mirror pairs of CalabiYau manifolds
 B. R. Greene, D. R. Morrison, and M. R. Plesser  Mirror manifolds in higher dimension
 S. Sethi  Supermanifolds, rigid manifolds and mirror symmetry
