Mirror Symmetry 1 (Ams/Ip Studies in Advanced Mathematics, V. 9)

This volume represents a new edition of the papers which were originally published in Essays on Mirror Manifolds. That volume has continued to be quite popular, and this new edition is supplemented by an additional volume, Mirror Symmetry 2, edited by B. Greene and myself. In this volume, we would like to address a number of errors which were found in the original: for example, the workshop on Mirror Manifolds at the Mathematical Sciences Research Institute took place in 1991, not 1911. The paper by Geir Ellingsrud and Stein A. Stromme has been withdrawn at the authors’ request. Meanwhile, P.M.H. Wilson’s paper on “Kahler Classes on Calabi- Yau Threefolds— an Informal Survey”; Sheldon Katz’s paper on “Rational Curves on Calabi- Yau Threefolds”; Ziv Ran’s paper on “Deformations of Calabi-Yau Kleinfolds”; and David R. Morrison’s paper on “Picard-Fuchs Equations and Mirror Maps for Hypersurfaces” have all been corrected per new drafts from the authors. We are quite pleased with the continuing interest in each of the papers in this volume and look forward to the continuing development of this field in the new century. S.-T. Yau Cambridge, MA This volume is an updated edition of Essays on Mirror Manifolds, the first book of papers published after the phenomenon of mirror symmetry was discovered. The two major groups who made the discovery reported their papers here. Greene, Plesser, and Candelas gave details on their findings; Witten gave his interpretation which was vital for future development. Vafa introduced the concept of quantum cohomology. Several mathematicians, including Katz, Morrison, Wilson, Roan, Tian, Hbsch, Yau, and Borcea discussed current knowledge about Calabi-Yau manifolds. Ferrara and his coauthors addressed special geometry and $N=2$ supergravity. Rocek proposed possible mirrors for Calabi-Yau manifolds with torsion. This collection continues to be an important book on this spectacular achievement in algebraic geometry and mathematical physics. Vol. 1 represents a new ed. of papers which were originally published in Essays on mirror manifolds (1992); supplemented by the additional volume: Mirror symmetry 2 which presents papers by both physicists and mathematicians. Mirror symmetry 1 (the 1st volume) constitutes the proceedings of the Mathematical Sciences Research Institute Workshop of 1991 This volume is an updated edition of "Essays on Mirror Manifolds", the first book of papers published after the phenomenon of mirror symmetry was discovered. The two major groups who made the discovery reported their papers here; contributors include Greene, Plesser, Candelas and Witten.