%0 Journal Article %T Irreducibility of the Gorenstein locus of the punctual Hilbert scheme of degree 10 %A Gianfranco Casnati %A Roberto Notari %J Mathematics %D 2010 %I arXiv %X 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. %U http://arxiv.org/abs/1003.5569v2