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On the Gorenstein locus of some punctual Hilbert schemes

2009; Elsevier BV; Volume: 213; Issue: 11 Linguagem: Inglês

10.1016/j.jpaa.2009.03.002

ISSN

1873-1376

Autores

Gianfranco Casnati, Roberto Notari,

Tópico(s)

Algebraic structures and combinatorial models

Resumo

Let k be an algebraically closed field and let HilbdG(PkN) be the open locus of the Hilbert scheme Hilbd(PkN) corresponding to Gorenstein subschemes. We prove that HilbdG(PkN) is irreducible for d≤9. Moreover we also give a complete picture of its singular locus in the same range d≤9. Such a description of the singularities gives some evidence to a conjecture on the nature of the singular points in HilbdG(PkN) that we state at the end of the paper.

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