{
  "id": "1111.2007",
  "version": "v3",
  "published": "2011-11-08T18:40:34.000Z",
  "updated": "2014-03-18T12:36:06.000Z",
  "title": "The locus of points of the Hilbert scheme with bounded regularity",
  "authors": [
    "Edoardo Ballico",
    "Cristina Bertone",
    "Margherita Roggero"
  ],
  "comment": "v2: new proofs relying on the functorial definition of the Hilbert scheme. v3: Sections reorganized, new self-contained proof of the representability of the Hilbert functor with bounded regularity (Section 6)",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we consider the Hilbert scheme $Hilb_{p(t)}^n$ parameterizing subschemes of $P^n$ with Hilbert polynomial $p(t)$, and we investigate its locus containing points corresponding to schemes with regularity lower than or equal to a fixed integer $r'$. This locus is an open subscheme of $Hilb_{p(t)}^n$ and, for every $s\\geq r'$, we describe it as a locally closed subscheme of the Grasmannian $Gr_{p(s)}^{N(s)}$ given by a set of equations of degree $\\leq \\mathrm{deg}(p(t))+2$ and linear inequalities in the coordinates of the Pl\\\"ucker embedding.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-18T12:36:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C05",
      "14Q20"
    ],
    "keywords": [
      "hilbert scheme",
      "bounded regularity",
      "locus containing points",
      "regularity lower",
      "open subscheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.2007B"
    }
  }
}