Log mirror symmetry and local mirror symmetry

Details Log mirror symmetry and local mirror symmetry Log mirror symmetry and local mirror symmetry

2000-04-28

arxiv.org/abs/math/0004179v1

Commun.Math.Phys. 220 (2001) 293-299

Mathematics

Algebraic Geometry

6 pages

Scientific paper

10.1007/PL00005567

We study Mirror Symmetry of log Calabi-Yau surfaces. On one hand, we consider the number of ``affine lines'' of each degree in the complement of a smooth cubic in the projective plane. On the other hand, we consider coefficients of a certain expansion of a function obtained from the integrals of dxdy/xy over 2-chains whose boundaries lie on B_\phi where {B_\phi} is a family of smooth cubics. Then, for small degrees, they coincide. We discuss the relation between this phenomenon and local mirror symmetry for projective plane in a Calabi-Yau 3-fold by Chiang-Klemm-Yau-Zaslow.

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