{
  "id": "1204.4418",
  "version": "v1",
  "published": "2012-04-19T17:37:43.000Z",
  "updated": "2012-04-19T17:37:43.000Z",
  "title": "The Picard group of a coarse moduli space of vector bundles in positive characteristic",
  "authors": [
    "Norbert Hoffmann"
  ],
  "comment": "8 pages. to appear in: Central European Journal of Mathematics",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let M_{r,L}^{ss} denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant L. We prove Pic(M_{r,L}^{ss}) = Z, identify the ample generator, and deduce that M_{r,L}^{ss} is locally factorial. In characteristic zero, this has already been proved by Dr\\'{e}zet and Narasimhan. The main point of the present note is to circumvent the usual problems with Geometric Invariant Theory in positive caracteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-19T17:37:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14H60"
    ],
    "keywords": [
      "coarse moduli space",
      "vector bundles",
      "picard group",
      "positive characteristic",
      "projective coarse moduli scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.4418H"
    }
  }
}