{
  "id": "1703.02703",
  "version": "v1",
  "published": "2017-03-08T05:02:44.000Z",
  "updated": "2017-03-08T05:02:44.000Z",
  "title": "A stratification of Hilbert schemes via generic initial ideals",
  "authors": [
    "Donghoon Hyeon"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the decompositions of Hilbert schemes induced by the Schubert cell decomposition of the Grassmannian variety and show that Hilbert schemes admit a stratification into locally closed subschemes along which the generic initial ideals remain the same. We give two applications: First, we give a completely geometric proofs of the existence of the generic initial ideals and of their Borel fixed properties. Secondly, we prove that when a Hilbert scheme is embedded by the Grothendieck-Pl\\\"ucker embedding of a high enough degree, one of its components must be degenerate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-08T05:02:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C05",
      "13P10"
    ],
    "keywords": [
      "stratification",
      "generic initial ideals remain",
      "hilbert schemes admit",
      "schubert cell decomposition",
      "geometric proofs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}