{
  "id": "0903.1029",
  "version": "v3",
  "published": "2009-03-05T16:45:51.000Z",
  "updated": "2011-01-21T16:22:39.000Z",
  "title": "Rational components of Hilbert schemes",
  "authors": [
    "Paolo Lella",
    "Margherita Roggero"
  ],
  "comment": "27 pages; Theorem 4.7 and final example strengthened; final version: accepted for publication on Rendiconti del Seminario Matematico dell'Universit\\`a di Padova",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "The Gr\\\"obner stratum of a monomial ideal $\\id{j}$ is an affine variety that parametrizes the family of all ideals having $\\id{j}$ as initial ideal (with respect to a fixed term ordering). The Gr\\\"obner strata can be equipped in a natural way of a structure of homogeneous variety and are in a close connection with Hilbert schemes of subvarieties in the projective space $\\PP^n$. Using properties of the Gr\\\"obner strata we prove some sufficient conditions for the rationality of components of $\\hilb_{p(z)}^n$. We show for instance that all the smooth, irreducible components in $\\hilb_{p(z)}^n$ (or in its support) and the Reeves and Stillman component $H_{RS}$ are rational.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-01-21T16:22:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C05"
    ],
    "keywords": [
      "hilbert schemes",
      "rational components",
      "close connection",
      "affine variety",
      "initial ideal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1029L"
    }
  }
}