Rational curves on Calabi-Yau threefolds

Abstract

This note is a survey of the enumerative geometry of rational curves on Calabi-Yau threefolds, based on a talk given by the author at the May 1991 Workshop on Mirror Symmetry at MSRI. An earlier version appeared in "Essays on Mirror Manifolds"; this version corrects typographical errors that appeared in print, gives a brief update of related progress during the last two years in the form of footnotes, and has more and updated references. (To appear in the second edition of Essays on Mirror Manifolds.)

15 pages, amstex (Replaced version contains new references and footnotes, and corrects a typographical error.)

References in corpus (4)

• Mirror Symmetry for Two Parameter Models -- II
• Considerations of One-Modulus Calabi-Yau Compactifications: Picard-Fuchs Equations, Kähler Potentials and Mirror Maps
• Enumeration of $n$-fold tangent hyperplanes to a surface
• Chern classes and degenerations of hypersurfaces and their lines

Cited by in corpus (6)

• Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
• Supersymmetric partition functions on Riemann surfaces
• Chiral Rings Do Not Suffice: N=(2,2) Theories with Nonzero Fundamental Group
• Direct integration for general Omega backgrounds
• Holomorphic Couplings In Non-Perturbative String Compactifications
• Calabi-Yau complete intersections with infinitely many lines