Families of K3 surfaces and curves of (2,3)-torus type

Abstract

We study families of K3 surfaces obtained by double covering of the projective plane branching along curves of (2,3)-torus type. In the first part, we study the Picard lattices of the families, and a lattice duality of them. In the second part, we describe a deformation of singularities of Gorenstein K3 surfaces in these families.