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.
"Families of $K3$ surfaces and curves of (2,3)-torus type." Kodai Math. J. 42 (3) 409 - 430, October 2019. https://doi.org/10.2996/kmj/1572487224