A note on simple K3 singularities and families of weighted K3 surfaces

Abstract

We discuss properties of the Seifert form for simple K3 singularities, and of the Picard lattices of families of weighted K3 surfaces. We study a collection $$\mathcal {M}_{(\rho ,\,\delta )}$$ of K3 surfaces polarized by their Picard lattices that are in the set $$\mathcal {L}_{(\rho ,\,\delta )}$$ of certain lattices. We also report a numerical formula that relates the Seifert form for the singularities and the Picard lattice of the family.