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

## TL;DR

This paper investigates families of K3 surfaces arising from double covers of the projective plane branched along (2,3)-torus type curves, analyzing their Picard lattices and deformations of singularities.

## Contribution

It introduces a detailed study of Picard lattices and dualities, and describes deformations of singularities in these specific K3 surface families.

## Key findings

- Identification of Picard lattice structures
- Description of lattice duality phenomena
- Analysis of singularity deformations in Gorenstein K3 surfaces

## 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.