On the geometry of singular K3 surfaces with discriminant 3, 4 and 7

Abstract

We give construction of singular K3 surfaces with discriminant 3 and 4 as double coverings over the projective plane. Focusing on the similarities in their branching loci, we can generalize this construction, and obtain a three dimensional moduli space of certain K3 surfaces which admit infinite automorphism groups. Moreover, we show that these K3 surfaces are characterized in terms of the configuration of the singular fibres and a global section, and also in terms of periods.