{
  "id": "math/0504500",
  "version": "v2",
  "published": "2005-04-25T11:18:07.000Z",
  "updated": "2005-07-11T08:50:11.000Z",
  "title": "The action of the Frobenius map on rank 2 vector bundles over a supersingular genus 2 curve in characteristic 2",
  "authors": [
    "Laurent Ducrohet"
  ],
  "comment": "15 pages, submitted in april 2005",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth proper genus 2 curve over an algebraically closed field of characteristic 2. The absolute Frobenius induces a rational map $F$ on the the moduli space $M\\_X$ of semi-stable rank 2 vector bundles over $X$, which is isomorphic to a 3-dimensional projective space. Y. Laszlo and C. Pauly recently gave the equations of $F$ for an ordinary $X$. Using deformation, we give these equations for a supersingular $X$ and draw some consequences such as the base locus of $F$ (one point), or the stability of the complementary Zariski open set.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-07-11T08:50:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60"
    ],
    "keywords": [
      "vector bundles",
      "supersingular genus",
      "frobenius map",
      "characteristic",
      "complementary zariski open set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4500D"
    }
  }
}