GIT Moduli Spaces of Certain Singular Cubic Fourfolds

R. Laza proved that a cubic fourfold (cubic hypersurface in the five dimensional projective space) with isolated singularities is stable in the sense of geometric invariant theory (GIT) if and only if it has at worst (ADE)-singularities. We can consequently construct the GIT (coarse) moduli space of those cubic fourfolds. This moduli space is then a quasi-projective variety. I am studying (coarse) moduli spaces of cubic fourfolds with certain isolated (ADE)-singularities and construct isomorphisms of those to the moduli spaces of certain K3 surfaces with a degree 6 line bundle.