{
  "id": "1101.5489",
  "version": "v1",
  "published": "2011-01-28T09:39:12.000Z",
  "updated": "2011-01-28T09:39:12.000Z",
  "title": "Tautological and non-tautological cohomology of the moduli space of curves",
  "authors": [
    "C. Faber",
    "R. Pandharipande"
  ],
  "comment": "40 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "After a short exposition of the basic properties of the tautological ring of the moduli space of genus g Deligne-Mumford stable curves with n markings, we explain three methods of detecting non-tautological classes in cohomology. The first is via curve counting over finite fields. The second is by obtaining length bounds on the action of the symmetric group S_n on tautological classes. The third is via classical boundary geometry. Several new non-tautological classes are found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-28T09:39:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "non-tautological cohomology",
      "deligne-mumford stable curves",
      "short exposition",
      "finite fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.5489F"
    }
  }
}