{
  "id": "1006.3653",
  "version": "v3",
  "published": "2010-06-18T09:44:43.000Z",
  "updated": "2013-01-08T19:38:39.000Z",
  "title": "Components of Gröbner strata in the Hilbert scheme of points",
  "authors": [
    "Mathias Lederer"
  ],
  "comment": "49 pages",
  "doi": "10.1112/plms/pdt018",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "We fix the lexicographic order $\\prec$ on the polynomial ring $S=k[x_{1},...,x_{n}]$ over a ring $k$. We define $\\Hi^{\\prec\\Delta}_{S/k}$, the moduli space of reduced Gr\\\"obner bases with a given finite standard set $\\Delta$, and its open subscheme $\\Hi^{\\prec\\Delta,\\et}_{S/k}$, the moduli space of families of $#\\Delta$ points whose attached ideal has the standard set $\\Delta$. We determine the number of irreducible and connected components of the latter scheme; we show that it is equidimensional over ${\\rm Spec}\\,k$; and we determine its relative dimension over ${\\rm Spec} k$. We show that analogous statements do not hold for the scheme $\\Hi^{\\prec\\Delta}_{S/k}$. Our results prove a version of a conjecture by Bernd Sturmfels.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-01-08T19:38:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C05",
      "14N10",
      "13P10",
      "13B25"
    ],
    "keywords": [
      "gröbner strata",
      "hilbert scheme",
      "components",
      "moduli space",
      "finite standard set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.3653L"
    }
  }
}