{
  "id": "math/0509451",
  "version": "v1",
  "published": "2005-09-20T13:02:58.000Z",
  "updated": "2005-09-20T13:02:58.000Z",
  "title": "The boundary of the Milnor fiber of Hirzebruch surface singularities",
  "authors": [
    "F. Michel",
    "Anne Pichon",
    "C. Weber"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We give the first (as far as we know) complete description of the boundary of the Milnor fiber for some non-isolated singular germs of surfaces in ${\\bf C}^3$. We study irreducible (i.e. $gcd (m,k,l) = 1$) non-isolated (i.e. $1 \\leq k < l$) Hirzebruch hypersurface singularities in ${\\bf C}^3$ given by the equation $z^m - x^ky^l = 0$. We show that the boundary $L$ of the Milnor fiber is always a Seifert manifold and we give an explicit description of the Seifert structure. From it, we deduce that : 1) $L$ is never diffeomorphic to the boundary of the normalization. 2) $L$ is a lens space iff $m = 2$ and $k = 1$. 3) When $L$ is not a lens space, it is never orientation preserving diffeomorphic to the boundary of a normal surface singularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-20T13:02:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J17",
      "32S25",
      "57M25"
    ],
    "keywords": [
      "milnor fiber",
      "hirzebruch surface singularities",
      "lens space",
      "normal surface singularity",
      "hirzebruch hypersurface singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9451M"
    }
  }
}