{
  "id": "math/0010319",
  "version": "v2",
  "published": "2000-10-31T17:25:17.000Z",
  "updated": "2002-08-05T18:25:39.000Z",
  "title": "Elementary Transversality in the Schubert calculus in any Characteristic",
  "authors": [
    "Frank Sottile"
  ],
  "comment": "14 pages, many revisions to improve clarity",
  "journal": "Michigan Math. J. 51 (2003), no. 3, 651-666",
  "categories": [
    "math.AG"
  ],
  "abstract": "We give a characteristic-free proof that general codimension-1 Schubert varieties meet transversally in a Grassmannian and in some related varieties. Thus the corresponding intersection numbers computed in the Chow (and quantum Chow) rings of these varieties are enumerative in all characteristics. We show that known transversality results do not apply to these enumerative problems, emphasizing the need for additional theoretical work on transversality. The method of proof also strengthens some results in real enumerative geometry.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-08-05T18:25:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N10",
      "14M15",
      "14N15",
      "14N35",
      "14P99"
    ],
    "keywords": [
      "schubert calculus",
      "elementary transversality",
      "corresponding intersection numbers",
      "characteristic-free proof",
      "schubert varieties meet"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....10319S"
    }
  }
}