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

We give a mathematical account of a recent string theory calcula- tion which predicts the number of rational curves on the generic quintic three- fold. 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" phe- nomenon recently observed by string theorists. DEPARTMENT OF MATHEMATICS, DUKE UNIVERSITY, DURHAM, NORTH CAROLINA 27706 E-mail address: drm@math.duke.edu This content downloaded from 157.55.39.224 on Wed, 14 Dec 2016 04:59:36 UTC All use subject to http://about.jstor.org/terms

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