{
  "id": "1103.4946",
  "version": "v3",
  "published": "2011-03-25T11:09:03.000Z",
  "updated": "2011-10-07T06:46:10.000Z",
  "title": "Explicit Solution By Radicals, Gonal Maps and Plane Models of Algebraic Curves of Genus 5 or 6",
  "authors": [
    "Michael Corin Harrison"
  ],
  "comment": "v3: full version of the paper",
  "categories": [
    "math.AG"
  ],
  "abstract": "We give explicit computational algorithms to construct minimal degree (always $\\le 4$) ramified covers of $\\Prj^1$ for algebraic curves of genus 5 and 6. This completes the work of Schicho and Sevilla (who dealt with the $g \\le 4$ case) on constructing radical parametrisations of arbitrary genus $g$ curves. Zariski showed that this is impossible for the general curve of genus $\\ge 7$. We also construct minimal degree birational plane models and show how the existence of degree 6 plane models for genus 6 curves is related to the gonality and geometric type of a certain auxiliary surface.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-10-07T06:46:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic curves",
      "explicit solution",
      "gonal maps",
      "construct minimal degree birational plane",
      "minimal degree birational plane models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.4946C"
    }
  }
}