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On the irreducibility and the singularities of the Gorenstein locus of the punctual Hilbert scheme of degree 10

2010; Elsevier BV; Volume: 215; Issue: 6 Linguagem: Inglês

10.1016/j.jpaa.2010.08.008

1873-1376

Gianfranco Casnati, Roberto Notari,

Algebraic structures and combinatorial models

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 a previous paper that HilbdG(PkN) is irreducible for d≤9 and N≥1. In the present paper we prove that Hilb10G(PkN) is irreducible for each N≥1, giving also a complete description of its singular locus.