{
  "id": "1502.03001",
  "version": "v1",
  "published": "2015-02-10T17:34:23.000Z",
  "updated": "2015-02-10T17:34:23.000Z",
  "title": "Connectivity of the branch locus of moduli space of rational maps",
  "authors": [
    "Ruben A. Hidalgo",
    "Saul Quispe"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The branch locus ${\\mathcal B}_{d}$ in moduli space ${\\rm M}_{d}$ of rational maps of degree $d \\geq 2$ consits of the equivalence classes of rational maps with non-trivial holomorphic automorphisms. Milnor proved that ${\\mathcal B}_{2}$ is a cubic curve; so connected. In this paper we see that ${\\mathcal B}_{d}$ is always connected. As, for $d \\geq 3$, the singular locus of ${\\rm M}_{d}$ equals the branch locus, this also provides the connectivity of that locus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-10T17:34:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37P45",
      "37F10",
      "37P05"
    ],
    "keywords": [
      "rational maps",
      "branch locus",
      "moduli space",
      "connectivity",
      "non-trivial holomorphic automorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150203001H"
    }
  }
}