{
  "id": "math/0111068",
  "version": "v1",
  "published": "2001-11-07T05:00:46.000Z",
  "updated": "2001-11-07T05:00:46.000Z",
  "title": "Frobenius pull-back and stability of vector bundles in characteristic 2",
  "authors": [
    "Jiu-Kang Yu",
    "Eugene Z. Xia"
  ],
  "comment": "pdf, 9 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a smooth projective curve of genus g>1 over an algebraically closed field of characteristic 2. Pull-back by the (absolute) Frobenius on X only defines a rational morphism on the moduli scheme of rank-2 vector bundles on X, because the Frobenius pull-back may destory stability of a vector bundle. This paper introduces and studies a Harder-Narasimhan type stratification on the moduli scheme and proves that the family of semi-stable rank-2 vector bundles (with a fixed degree) whose Frobenius pull-back are not semi-stable is parameterized by an irreducible subscheme of dimension 3g-4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-11-07T05:00:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14H60"
    ],
    "keywords": [
      "vector bundle",
      "frobenius pull-back",
      "characteristic",
      "moduli scheme",
      "harder-narasimhan type stratification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}