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, Hübsch, Yau, and Borcea discussed current knowledge about Calabi-Yau manifolds. Ferrara and his coauthors addressed special geometry and \(N=2\) supergravity. Roček 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.

Also available from the AMS are the related volumes, Mirror Symmetry II (1996), 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 mathematical physicists working in algebraic geometry, mathematical physics, and number theory.

Reviews

From a review of the first edition ...

"This volume is very timely, giving very broad coverage of one of the important developments in mathematics and physics today ... This volume is a requisite for those working in the area of CY \(3\)-folds, as well as those interested in mathematical implications of contemporary physics."

-- Mathematical Reviews

Table of Contents

• B. R. Greene and M. R. Plesser -- An introduction to mirror manifolds
• P. Candelas, X. C. de la Ossa, P. S. Green, and L. Parkes -- A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
• C. Vafa -- Topological mirrors and quantum rings
• E. Witten -- Mirror manifolds and topological field theory
• Y. Kawamata -- Rational curves and classification of algebraic varieties
• S. Katz -- Rational curves on Calabi-Yau threefolds
• D. R. Morrison -- Picard-Fuchs equations and mirror maps for hypersurfaces
• P. M. H. Wilson -- Kähler classes on Calabi-Yau threefolds--An informal survey
• S. Ferrara, C. Kounnas, D. Lüst, and F. Zwirner -- Automorphic functions and special Kähler geometry
• S. Ferrara and J. Louis -- Picard-Fuchs equations and flat holomorphic connections from \(N = 2\) supergravity
• P. S. Aspinwall and C. A. Lutken -- A new geometry from superstring theory
• S.-S. Roan -- The geometry of Calabi-Yau orbifolds
• A. Giveon and D.-J. Smit -- Properties of superstring vacua from (topological) Landau-Ginzburg models
• T. Hübsch and S.-T. Yau -- An \(SL(2,\mathbb{C})\) action on certain Jacobian rings and the mirror map
• P. Berglund and T. Hübsch -- A generalized construction of mirror manifolds
• B. R. Greene, M. R. Plesser, and S.-S. Roan -- New constructions of mirror manifolds: Probing moduli space far from Fermat points
• Z. Ran -- Deformations of Calabi-Yau Kleinfolds
• G. Tian -- Smoothing 3-folds with trivial canonical bundle and ordinary double points
• M. Roček -- Modified Calabi-Yau manifolds with torsion
• C. Borcea -- Calabi-Yau threefolds and complex multiplication