On the Gorenstein locus of the punctual Hilbert scheme of degree 11

Let k   be an algebraically closed field of characteristic 0 and let HilbdG(PkN) be the open locus of the Hilbert scheme Hilbd(PkN) corresponding to Gorenstein subschemes. We proved in several previous papers that HilbdG(PkN) is irreducible for d⩽10d⩽10 and N⩾1N⩾1, characterizing its singular locus. In the present paper we prove that also Hilb11G(PkN) is irreducible for each N⩾1N⩾1. We also give some results about its singular locus.