Log Mirror Symmetry and Local Mirror Symmetry
Abstract
We study Mirror Symmetry of log CalabiYau 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 2chains 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 CalabiYau 3fold by ChiangKlemmYauZaslow.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2001
 DOI:
 10.1007/PL00005567
 arXiv:
 arXiv:math/0004179
 Bibcode:
 2001CMaPh.220..293T
 Keywords:

 Mathematics  Algebraic Geometry;
 14N10
 EPrint:
 6 pages