Moduli of K3 surfaces of degree 2 with four rational double points of type $D_4$

Abstract

We show that the Satake-Baily-Borel compactification of the moduli space of lattice polarized K3 surfaces parametrizing K3 surfaces of degree 2 with four rational double points of type $D_4$ is the projective 3-space. We also show that the corresponding graded ring of automorphic forms is generated by four elements of weight 2 and one element of weight 11 with one relation of weight 22.