Making enumerative predictions by means of mirror symmetry

Abstract

Given two Calabi--Yau threefolds which are believed to constitute a mirror pair, there are very precise predictions about the enumerative geometry of rational curves on one of the manifolds which can be made by performing calculations on the other. We review the mechanics of making these predictions, including a discussion of two conjectures which specify how the elusive ``constants of integration'' in the mirror map should be fixed. Such predictions can be useful for checking whether or not various conjectural constructions of mirror manifolds are producing reasonable answers.

24 pages with 2 figures

References in corpus (1)

• Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties

Cited by in corpus (10)

• D-Branes on Calabi-Yau Spaces and Their Mirrors
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• The Geometry Underlying Mirror Symmetry
• Small Volumes in Compactified String Theory
• Mirror Symmetry and the Type II String
• String Cohomology of a Toroidal Singularity
• Gauss-Bonnet-Chern theorem on moduli space
• String Duality and Enumeration of Curves by Jacobi Forms
• A Hall of Statistical Mirrors