{
  "id": "1403.7399",
  "version": "v3",
  "published": "2014-03-28T14:48:16.000Z",
  "updated": "2015-08-16T09:37:19.000Z",
  "title": "Mapping Class Groups of Trigonal Loci",
  "authors": [
    "Michele Bolognesi",
    "Michael Lönne"
  ],
  "comment": "To appear on Selecta Math",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we study the topology of the stack $\\mathcal{T}_g$ of smooth trigonal curves of genus g, over the complex field. We make use of a construction by the first named author and Vistoli, that describes $\\mathcal{T}_g$ as a quotient stack of the complement of the discriminant. This allows us to use techniques developed by the second named author to give presentations of the orbifold fundamental group of $\\mathcal{T}_g$, of its substrata with prescribed Maroni invariant and describe their relation with the mapping class group $\\mathcal{M}ap_g$ of Riemann surfaces of genus g.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-10T21:28:45.000Z",
      "comment": "Preliminary version, comments welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-08-16T09:37:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mapping class group",
      "trigonal loci",
      "orbifold fundamental group",
      "smooth trigonal curves",
      "riemann surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7399B"
    }
  }
}