{
  "id": "math/0010182",
  "version": "v1",
  "published": "2000-10-18T04:17:45.000Z",
  "updated": "2000-10-18T04:17:45.000Z",
  "title": "Fundamental group of sextics of torus type",
  "authors": [
    "Mutsuo Oka",
    "Duc Tai Pho"
  ],
  "comment": "27 pages, 14 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that the fundamental group of the complement of any irreducible tame torus sextics in $\\bf P^2$ is isomorphic to $\\bf Z_2*\\bf Z_3$ except one class. The exceptional class has the configuration of the singularities $\\{C_{3,9},3A_2\\}$ and the fundamental group is bigger than $\\bf Z_2*\\bf Z_3$. In fact, the Alexander polynomial is given by $(t^2-t+1)^2$. For the proof, we first reduce the assertion to maximal curves and then we compute the fundamental groups for maximal tame torus curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-10-18T04:17:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H30",
      "14H45",
      "32S55"
    ],
    "keywords": [
      "fundamental group",
      "torus type",
      "maximal tame torus curves",
      "irreducible tame torus sextics",
      "exceptional class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....10182O"
    }
  }
}