Abstract

Inspired by the works of Hitchin and Huybrechts, we introduce a formulation of mirror symmetry for generalized K3 surfaces by Mukai lattice polarizations. This formulation is compatible with the SCFT on K3 surfaces discussed by Aspinwall-Morrison, and fixes the problems in the conventional mirror symmetry for lattice polarized K3 surfaces. In particular, we settle the long-standing problem of mirror symmetry for singular K3 surfaces (also known as rigid K3 surfaces).