{
  "id": "1102.0490",
  "version": "v1",
  "published": "2011-02-02T16:58:05.000Z",
  "updated": "2011-02-02T16:58:05.000Z",
  "title": "Irreducibility of the space of dihedral covers of the projective line of a given numerical type",
  "authors": [
    "Fabrizio Catanese",
    "Michael Lönne",
    "Fabio Perroni"
  ],
  "comment": "18 pages, to appear in Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., volume in memory of Giovanni Prodi",
  "categories": [
    "math.AG",
    "math.GT"
  ],
  "abstract": "We show in this paper that the set of irreducible components of the family of Galois coverings of P^1_C with Galois group isomorphic to D_n is in bijection with the set of possible numerical types. In this special case the numerical type is the equivalence class (for automorphisms of D_n) of the function which to each conjugacy class \\mathcal{C} in D_n associates the number of branch points whose local monodromy lies in the class \\mathcal{C}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-02T16:58:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "20F36",
      "57M12"
    ],
    "keywords": [
      "numerical type",
      "dihedral covers",
      "projective line",
      "irreducibility",
      "galois group isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.0490C"
    }
  }
}