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

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.