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arXiv · 1003.5569

Irreducibility of the Gorenstein locus of the punctual Hilbert scheme of degree 10

Gianfranco Casnati·Roberto Notari
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Abstract

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

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Gianfranco Casnati, Roberto Notari. 2010-03-30. Irreducibility of the Gorenstein locus of the punctual Hilbert scheme of degree 10. https://arxiv.org/abs/1003.5569

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