{
  "id": "1801.00465",
  "version": "v1",
  "published": "2018-01-01T16:01:39.000Z",
  "updated": "2018-01-01T16:01:39.000Z",
  "title": "Hyperbolic 2-spheres with cone singularities",
  "authors": [
    "Sasha Anan'in",
    "Carlos H. Grossi",
    "Jaejeong Lee",
    "João dos Reis jr"
  ],
  "comment": "21 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We study the space $C(a_0,a_1,\\dots,a_n)$ of hyperbolic 2-spheres with cone points of prescribed apex curvatures $2a_0,2a_1,\\dots,2a_n\\in]0,2\\pi[$ and some related spaces. For $n=3$, we get a detailed description of such spaces. The euclidean 2-spheres were considered by W. P. Thurston: for $n=4$, the corresponding spaces provide the famous 7 examples of nonarithmetic compact holomorphic 2-ball quotients previously constructed by Deligne-Mostow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-01T16:01:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F60",
      "22E40",
      "20H10"
    ],
    "keywords": [
      "cone singularities",
      "hyperbolic",
      "nonarithmetic compact holomorphic",
      "cone points",
      "prescribed apex curvatures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}