Mirror symmetry and ℂ^{×}

Takahashi, Nobuyoshi

doi:10.1090/S0002-9939-00-05901-3

Mirror symmetry and $\mathbb {C}^\times$
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by Nobuyoshi Takahashi PDF

Proc. Amer. Math. Soc. 129 (2001), 29-36 Request permission

Abstract:

We show that counting functions of covers of $\mathbb {C}^\times$ are equal to sums of integrals associated to certain ‘Feynman’ graphs. This is an analogue of the mirror symmetry for elliptic curves.

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