On some Gorenstein loci in Hilb6(Pk4)

AbstractLet k be an algebraically closed field and let HilbdaG(Pkd−2) be the open locus inside the Hilbert scheme Hilbd(Pkd−2) corresponding to arithmetically Gorenstein subschemes. We prove the irreducibility and characterize the singularities of Hilb6aG(Pk4). In order to achieve these results we also classify all Artinian, Gorenstein, not necessarily graded, k-algebras up to degree 6. Moreover, we describe the loci in Hilb6aG(Pk4) obtained via some geometric construction. Finally we prove the obstructedness of some families of points in HilbdaG(Pkd−2) for each d⩾6