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Mirror symmetry II
Edited by: B. Greene, Cornell University, Ithaca, NY, and S.-T. Yau, Harvard University, Cambridge, MA
A co-publication of the AMS and International Press.
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AMS/IP Studies in Advanced Mathematics
1996; 844 pp; softcover
Volume: 1
Reprint/Revision History:
reprinted 2001
ISBN-10: 0-8218-2744-8
ISBN-13: 978-0-8218-2744-4
List Price: US$103
Member Price: US$82.40
Order Code: AMSIP/1.S
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See also:

Mirror Symmetry I - Shing-Tung Yau

Mirror Symmetry III - Duong H Phong, Luc Vinet and Shing-Tung Yau

Mirror Symmetry IV - Eric D'Hoker, Duong Phong and Shing-Tung Yau

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 co-published with International Press, 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 -- Calabi-Yau 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 -- Picard-Fuchs 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 Calabi-Yau classification--a preliminary survey
  • Z. Ran -- Thickening Calabi-Yau moduli spaces
  • M. Gross -- The deformation space of Calabi-Yau \(n\)-folds with canonical singularities can be obstructed
  • A. Giveon and M. Roček -- Introduction to duality
  • E. Kiritsis, C. Kounnas, and D. Lüst -- Non-compact Calabi-Yau spaces and other non-trivial backgrounds for four-dimensional superstrings
  • R. Schimmrigk -- Scaling behavior on the space of Calabi-Yau 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 models--I
  • S. Hosono, A. Klemm, S. Theisen, and S.-T. Yau -- Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces
  • M. Kontsevich and Yu. Manin -- Gromov-Witten 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 Calabi-Yau manifolds
  • B. R. Greene, D. R. Morrison, and M. R. Plesser -- Mirror manifolds in higher dimension
  • S. Sethi -- Supermanifolds, rigid manifolds and mirror symmetry
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