Abstract:
We study Mirror Symmetry of log Calabi–Yau surfaces. On one hand, we consider the number of “affine lines” of each degree in ℙ2\B, where B is a smooth cubic. On the other hand, we consider coefficients of a certain expansion of a function obtained from the integrals of dx/x∧dy/y over 2-chains whose boundaries lie on B φ, where {B φ} is a family of smooth cubics. Then, for small degrees, they coincide.
We discuss the relation between this phenomenon and local mirror symmetry for ℙ2 in a Calabi–Yau 3-fold ([CKYZ]).
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Received: 1 October 1999 / Accepted: 22 November 2000
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Takahashi, N. Log Mirror Symmetry and Local Mirror Symmetry. Commun. Math. Phys. 220, 293–299 (2001). https://doi.org/10.1007/PL00005567
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DOI: https://doi.org/10.1007/PL00005567