{
  "id": "math/0504249",
  "version": "v3",
  "published": "2005-04-12T16:38:44.000Z",
  "updated": "2007-01-17T10:37:21.000Z",
  "title": "On the rationality of moduli spaces of pointed curves",
  "authors": [
    "Gianfranco Casnati",
    "Claudio Fontanari"
  ],
  "comment": "Final version accepted for publication on the Journal of the London Mathematical Society (Section 6 of the previous version has been removed since the proof of Claim 6.3 contained a gap)",
  "categories": [
    "math.AG"
  ],
  "abstract": "Motivated by several recent results on the geometry of the moduli spaces $\\bar{\\Cal M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points, here we determine their birational structure for small values of $g$ and $n$ by exploiting suitable plane models of the general curve. More precisely, we show that ${\\Cal M}_{g,n}$ is rational for $g=2$ and $1\\le n\\le 12$, $g=3$ and $1\\le n\\le 14$, $g=4$ and $1\\le n\\le 15$, $g=5$ and $1\\le n\\le 12$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-01-17T10:37:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14H45",
      "14E08",
      "14L30"
    ],
    "keywords": [
      "moduli spaces",
      "pointed curves",
      "rationality",
      "birational structure",
      "small values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4249C"
    }
  }
}