{
  "id": "math/9910014",
  "version": "v1",
  "published": "1999-10-04T15:12:59.000Z",
  "updated": "1999-10-04T15:12:59.000Z",
  "title": "Moduli of Vector Bundles on Curves in Positive Characteristics",
  "authors": [
    "Kirti Joshi",
    "Eugene Z. Xia"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli scheme of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 (with determinant equal to a theta characteristic) whose Frobenius pull-back is not semi-stable. The indeterminacy of the Frobenius map at this point can be resolved by introducing Higgs bundles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-10-04T15:12:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14H60"
    ],
    "keywords": [
      "positive characteristics",
      "frobenius map",
      "introducing higgs bundles",
      "frobenius pull-back",
      "theta characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....10014J"
    }
  }
}