{
  "id": "1610.09612",
  "version": "v1",
  "published": "2016-10-30T07:05:38.000Z",
  "updated": "2016-10-30T07:05:38.000Z",
  "title": "Fundamental group of Galois covers of degree 5 surfaces",
  "authors": [
    "Meirav Amram",
    "Cheng Gong",
    "Mina Teicher",
    "Wan-Yuan Xu"
  ],
  "comment": "29 pages, many figures",
  "categories": [
    "math.AT",
    "math.AG",
    "math.GR"
  ],
  "abstract": "Let $X$ be a surface of degree $5$, which is considered as a branch cover of $\\mathbb{CP}^2$ with respect to a generic projection. The surface has a natural Galois cover with Galois group $S_n$. In this paper, we compute the fundamental groups of Galois covers of degree $5$ that degenerate to nice plane arrangements; each of them is a union of five planes such that no three planes meet in a line. As an application, we give a counter-example of a question of Liedtke \\cite[Question\\,3.4]{Li08}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-30T07:05:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental group",
      "nice plane arrangements",
      "natural galois cover",
      "generic projection",
      "branch cover"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}