{
  "id": "math/0410037",
  "version": "v1",
  "published": "2004-10-03T01:10:42.000Z",
  "updated": "2004-10-03T01:10:42.000Z",
  "title": "A note on Hilbert schemes of nodal curves",
  "authors": [
    "Ziv Ran"
  ],
  "comment": "16 pages, 1 figure",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study completely the Hilbert scheme and punctual Hilbert scheme of a nodal curve, and the relative Hilbert scheme of a family of curves acquiring a node. The results are then extended, less completely, to flag Hilbert schemes, parametrizing chains of subschemes. We find, notably, that if the total space $X$ of a family $X/B$ is smooth (over an algebraically closed field $\\k$), then the relative Hilbert scheme $Hilb_m(X/B)$ is smooth over $\\k$ and the flag Hilbert schemes are normal and locally complete intersection, but generally singular.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-03T01:10:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C05"
    ],
    "keywords": [
      "nodal curve",
      "flag hilbert schemes",
      "relative hilbert scheme",
      "punctual hilbert scheme",
      "locally complete intersection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10037R"
    }
  }
}