{
  "id": "math/0108071",
  "version": "v1",
  "published": "2001-08-09T22:28:15.000Z",
  "updated": "2001-08-09T22:28:15.000Z",
  "title": "Multiplicities of Singular Points in Schubert Varieties of Grassmannians",
  "authors": [
    "V. Kreiman",
    "V. Lakshmibai"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We give a closed-form formula for the Hilbert function of the tangent cone at the identity of a Schubert variety X in the Grassmannian in both group theoretic and combinatorial terms. We also give a formula for the multiplicity of X at the identity, and a Grobner basis for the ideal defining the intersection of X with the opposite cell as a closed subvariety of the opposite cell. We give conjectures for the Hilbert function and multiplicity at points other than the identity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-08-09T22:28:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15"
    ],
    "keywords": [
      "schubert variety",
      "singular points",
      "multiplicity",
      "grassmannian",
      "opposite cell"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......8071K"
    }
  }
}