Mirror symmetry for log Calabi-Yau surfaces I 论文

摘要

We give a canonical synthetic construction of the mirror family to pairs ( Y , D ) where Y is a smooth projective surface and D is an anti-canonical cycle of rational curves. This mirror family is constructed as the spectrum of an explicit algebra structure on a vector space with canonical basis and multiplication rule defined in terms of counts of rational curves on Y meeting D in a single point. The elements of the canonical basis are called theta functions . Their construction depends crucially on the Gromov-Witten theory of the pair ( Y , D ).