{
  "id": "math/0312366",
  "version": "v2",
  "published": "2003-12-18T16:25:15.000Z",
  "updated": "2004-02-02T09:35:36.000Z",
  "title": "Non hyperelliptic curves of genus three over finite fields of characteristic two",
  "authors": [
    "Enric Nart",
    "Christophe Ritzenthaler"
  ],
  "comment": "31 pages ; added references ; the analysis of the supersingular locus has been modified",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let k=F_q be a finite field of even characteristic. We obtain in this paper a complete classification, up to k-isomorphism, of non singular quartic plane curves defined over k. We find explicit rational normal models and we give closed formulas for the total number of k-isomorphism classes. We deduce from these computations the number of k-rational points of the different strata by the Newton polygon of the non hyperelliptic locus M_3^{nh} of the moduli space M_3 of curves of genus 3. By adding to these computations the knowed results on the hyperelliptic locus we obtain a complete picture of these strata for M_3.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-02-02T09:35:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "14Q05",
      "14H10",
      "14H37"
    ],
    "keywords": [
      "non hyperelliptic curves",
      "finite field",
      "characteristic",
      "non singular quartic plane curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12366N"
    }
  }
}