Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians

Details Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians

1992-02-10

arxiv.org/abs/alg-geom/9202004v1

J. Amer. Math. Soc. 6 (1993) 223--247

Mathematics

Algebraic Geometry

26 pp., AmS-LaTeX (v1.0 or 1.1)

Scientific paper

We give a mathematical account of a recent string theory calculation which predicts the number of rational curves on the generic quintic threefold. Our account involves the interpretation of Yukawa couplings in terms of variations of Hodge structure, a new $q$-expansion principle for functions on the moduli space of Calabi-Yau manifolds, and the ``mirror symmetry'' phenomenon recently observed by string theorists.

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