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

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 $d\le 9$ and $N\ge 1$. In the present paper we prove that also $H_G(10,N)$ is irreducible for each $N\ge 1$, giving also a complete description of its singular locus.

An error in Proposition 5.9 has been corrected.

References in corpus (1)

• Isomorphism classes of certain Artinian Gorenstein algebras

Cited by in corpus (1)

• Local finite dimensional Gorenstein k-algebras having Hilbert function (1,5,5,1) are smoothable