Let $k$ be an algebraically closed field of characteristic $0$ and let $\Hilb_{d}^{G}(\p{N})$ be the open locus of the Hilbert scheme $\Hilb_{d}(\p{N})$ corresponding to Gorenstein subschemes. We proved in a previous paper that $\Hilb_{d}^{G}(\p{N})$ is irreducible for $d\le9$ and $N\ge1$. In the present paper we prove that also $\Hilb_{10}^{G}(\p{N})$ is irreducible for each $N\ge1$, giving also a complete description of its singular locus.

On the irriducibility and singularities of the Gorenstein locus of the punctual Hilbert scheme of degree 10 / Casnati, Gianfranco; Notari, Roberto. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - 215:6(2011), pp. 1243-1254. [10.1016/j.jpaa.2010.08.008]

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

CASNATI, GIANFRANCO;NOTARI, ROBERTO
2011

Abstract

Let $k$ be an algebraically closed field of characteristic $0$ and let $\Hilb_{d}^{G}(\p{N})$ be the open locus of the Hilbert scheme $\Hilb_{d}(\p{N})$ corresponding to Gorenstein subschemes. We proved in a previous paper that $\Hilb_{d}^{G}(\p{N})$ is irreducible for $d\le9$ and $N\ge1$. In the present paper we prove that also $\Hilb_{10}^{G}(\p{N})$ is irreducible for each $N\ge1$, giving also a complete description of its singular locus.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2371288
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