{
  "id": "1710.09594",
  "version": "v1",
  "published": "2017-10-26T08:52:26.000Z",
  "updated": "2017-10-26T08:52:26.000Z",
  "title": "The fundamental group of the complement of the singular locus of Lauricella's $F_C$",
  "authors": [
    "Yoshiaki Goto",
    "Jyoichi Kaneko"
  ],
  "comment": "50 pages, 27 figures",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "We study the fundamental group of the complement of the singular locus of Lauricella's hypergeometric function $F_C$ of $n$ variables. The singular locus consists of $n$ hyperplanes and a hypersurface of degree $2^{n-1}$ in the complex $n$-space. We give a conjectural presentation of the fundamental group, and prove it in the three-dimensional case. We also consider a presentation of the fundamental group of $2^3$-covering of this space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-26T08:52:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F35",
      "57M05",
      "57M10"
    ],
    "keywords": [
      "fundamental group",
      "complement",
      "lauricellas hypergeometric function",
      "singular locus consists",
      "conjectural presentation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}