{
  "id": "math/0208096",
  "version": "v1",
  "published": "2002-08-13T03:27:29.000Z",
  "updated": "2002-08-13T03:27:29.000Z",
  "title": "On vector bundles destabilized by Frobenius pull-back",
  "authors": [
    "Kirti Joshi",
    "S. Ramanan",
    "Eugene Z. Xia",
    "Jiu-Kang Yu"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be an irreducible smooth projective curve of genus at least two over an algebraically closed field k of characteristic p>0. In this paper we study the natural stratification, defined using the absolute Frobenius of X, on the moduli space of vector bundles on X of suitable rank. In characteristic two we provide a complete classification of rank two semi-stable vector bundles whose Frobenius pull-back is not semi-stable. We also obtain fairly good information about the strata of the Frobenius stratification, including the irreducibility and the dimension of each non-empty Frobenius stratum. In particular we show that the locus of Frobenius destabilized bundles has dimension 3g-4 in the moduli space of semi-stable bundles of rank two. We also construct stable bundles that are destabilized by Frobenius in the following situations: characteristic p=2 and rank four, (2) characteristic p=rank=3, (3) characteristic p=rank=5 and g at least three. We also explore (in any characteristic) the connection between Frobenius destabilized bundles and (pre)-opers, this approach allows us to reinterpret some of our results in terms of pre-opers and also allows us to construct Frobenius destablised bundles from certain pre-opers (or opers). The other result we obtain is (for characteristic two): we show that the Gunning bundle descends under Frobenius when genus g is even. If g is odd, then the Gunning bundle twisted by any odd degree line bundle also descends.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-08-13T03:27:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20"
    ],
    "keywords": [
      "frobenius pull-back",
      "vector bundles",
      "characteristic",
      "frobenius destabilized bundles",
      "odd degree line bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......8096J"
    }
  }
}