{
  "id": "math/0208031",
  "version": "v1",
  "published": "2002-08-05T06:21:31.000Z",
  "updated": "2002-08-05T06:21:31.000Z",
  "title": "The toric Hilbert scheme of a rank two lattice is smooth and irreducible",
  "authors": [
    "Diane Maclagan",
    "Rekha R. Thomas"
  ],
  "comment": "19 pages, 4 figures",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "The toric Hilbert scheme of a lattice L in Z^n is the multigraded Hilbert scheme parameterizing all ideals in k[x_1,...,x_n] with Hilbert function value one for every degree in the grading monoid N^n/L. In this paper we show that if L is two-dimensional, then the toric Hilbert scheme of L is smooth and irreducible. This result is false for lattices of dimension three and higher as the toric Hilbert scheme of a rank three lattice can be reducible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-08-05T06:21:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "toric hilbert scheme",
      "irreducible",
      "hilbert function value",
      "multigraded hilbert scheme parameterizing",
      "grading monoid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......8031M"
    }
  }
}