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

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

2010-03-29

arxiv.org/abs/1003.5569v2

Mathematics

Algebraic Geometry

An error in Proposition 5.9 has been corrected.

Scientific paper

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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