{
  "id": "0809.2981",
  "version": "v2",
  "published": "2008-09-17T19:12:56.000Z",
  "updated": "2009-09-04T21:19:20.000Z",
  "title": "Presenting the cohomology of a Schubert variety",
  "authors": [
    "Victor Reiner",
    "Alexander Woo",
    "Alexander Yong"
  ],
  "comment": "22 pages",
  "journal": "Trans. Amer. Math. Soc. 363 (2011), 521-543",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "We extend the short presentation due to [Borel '53] of the cohomology ring of a generalized flag manifold to a relatively short presentation of the cohomology of any of its Schubert varieties. Our result is stated in a root-system uniform manner by introducing the essential set of a Coxeter group element, generalizing and giving a new characterization of [Fulton '92]'s definition for permutations. Further refinements are obtained in type A.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-04T21:19:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "14N15"
    ],
    "keywords": [
      "schubert variety",
      "cohomology",
      "coxeter group element",
      "root-system uniform manner",
      "generalized flag manifold"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.2981R"
    }
  }
}