{
  "id": "1003.5569",
  "version": "v2",
  "published": "2010-03-29T15:25:25.000Z",
  "updated": "2010-03-30T15:01:23.000Z",
  "title": "Irreducibility of the Gorenstein locus of the punctual Hilbert scheme of degree 10",
  "authors": [
    "Gianfranco Casnati",
    "Roberto Notari"
  ],
  "comment": "An error in Proposition 5.9 has been corrected.",
  "categories": [
    "math.AG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-30T15:01:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "punctual hilbert scheme",
      "gorenstein locus",
      "irreducibility",
      "complete description",
      "singular locus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.5569C"
    }
  }
}