Let k be an algebraically closed field of characteristic 0 and let Hilb_d^G(P_k^N) be the open locus of the Hilbert scheme Hilb_d(P_k^N) corresponding to Gorenstein subschemes. We proved in several previous papers that Hilb_d^G(P_k^N) is irreducible for d⩽10 and N⩾1, characterizing its singular locus. In the present paper we prove that also Hilb_{11}^G(P_k^N) is irreducible for each N⩾1. We also give some results about its singular locus.
On the Gorenstein locus of the punctual Hilbert scheme of degree 11
NOTARI, ROBERTO
2014-01-01
Abstract
Let k be an algebraically closed field of characteristic 0 and let Hilb_d^G(P_k^N) be the open locus of the Hilbert scheme Hilb_d(P_k^N) corresponding to Gorenstein subschemes. We proved in several previous papers that Hilb_d^G(P_k^N) is irreducible for d⩽10 and N⩾1, characterizing its singular locus. In the present paper we prove that also Hilb_{11}^G(P_k^N) is irreducible for each N⩾1. We also give some results about its singular locus.File in questo prodotto:
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On the Gorenstein locus_11311-873154_Notari.pdf
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