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


Author: David R. Morrison
Journal: J. Amer. Math. Soc. 6 (1993), 223-247
MSC: Primary 14J30; Secondary 14D07, 14J15, 32G20, 32G81, 32J17
DOI: https://doi.org/10.1090/S0894-0347-1993-1179538-2
MathSciNet review: 1179538
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Abstract: 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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DOI: https://doi.org/10.1090/S0894-0347-1993-1179538-2
Article copyright: © Copyright 1993 American Mathematical Society

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