{
  "id": "1401.0179",
  "version": "v2",
  "published": "2013-12-31T16:55:41.000Z",
  "updated": "2014-07-02T09:18:36.000Z",
  "title": "Combinatorial duality of Hilbert schemes of points in the affine plane",
  "authors": [
    "Mathias Lederer"
  ],
  "comment": "16 pages, 8 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "The Hilbert scheme of $n$ points in the affine plane contains the open subscheme parametrizing $n$ distinct points in the affine plane, and the closed subscheme parametrizing ideals of codimension $n$ supported at the origin of the affine plane. Both schemes admit Bia{\\l}ynicki-Birula decompositions into moduli spaces of ideals with prescribed lexicographic Gr\\\"obner deformations. We show that both decompositions are stratifications in the sense that the closure of each stratum is a union of certain other strata. We show that the corresponding two partial orderings on the set of of monomial ideals are dual to each other.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-02T09:18:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C05",
      "13F20",
      "13P10",
      "06A11",
      "57N80"
    ],
    "keywords": [
      "hilbert scheme",
      "combinatorial duality",
      "affine plane contains",
      "monomial ideals",
      "distinct points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0179L"
    }
  }
}