Let k be an algebraically closed field and let $ Hilb^G_d(P^N_k) $ be the open locus of the Hilbert scheme $ Hilb_d(P^N_k) $ corresponding to Gorenstein subschemes. We prove that $ Hilb^G_d(P^N_k) $ is irreducible for $ d \leq 9 $. Moreover we also give a complete picture of its singular locus in the same range d \leq 9. Such a description of the singularities gives some evidence to a conjecture on the nature of the singular points in $ Hilb^G_d(P^N_k) $ that we state at the end of the paper.
On the Gorenstein locus of some punctual Hilbert schemes
NOTARI, ROBERTO
2009-01-01
Abstract
Let k be an algebraically closed field and let $ Hilb^G_d(P^N_k) $ be the open locus of the Hilbert scheme $ Hilb_d(P^N_k) $ corresponding to Gorenstein subschemes. We prove that $ Hilb^G_d(P^N_k) $ is irreducible for $ d \leq 9 $. Moreover we also give a complete picture of its singular locus in the same range d \leq 9. Such a description of the singularities gives some evidence to a conjecture on the nature of the singular points in $ Hilb^G_d(P^N_k) $ that we state at the end of the paper.File in questo prodotto:
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