📝 SummarXiv

Abstract

Using Geometric Invariant Theory, we compactify the moduli space of stable cubic fivefolds by adjoining strictly semistable hypersurfaces. We prove that the strictly semistable locus decomposes into twenty-one irreducible components and provide an explicit closed-orbit representative for each. Our Jacobian computations show that wild isolated hypersurface singularities already occur along the boundary such as quasi-homogeneous types of corank 3 and 4, thereby marking dimension five as a threshold beyond the ADE paradigm known for cubic threefolds and fourfolds. We also record adjacency relations among boundary components as wall crossings in Kirwan's stratification.