{
  "id": "math/0605123",
  "version": "v1",
  "published": "2006-05-04T13:51:40.000Z",
  "updated": "2006-05-04T13:51:40.000Z",
  "title": "The boundary of the Milnor fiber for some non-isolated germs of complex surfaces",
  "authors": [
    "Francoise Michel",
    "Anne Pichon",
    "Claude Weber"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AG",
    "math.GT"
  ],
  "abstract": "We study the boundary L_t of the Milnor fiber for the non-isolated singularities in C^3 with equation z^m - g(x,y) = 0 where g(x,y) is a non-reduced plane curve germ. We give a complete proof that L_t is a Waldhausen graph manifold and we provide the tools to construct its plumbing graph. As an example, we give the plumbing graph associated to the germs z^2 - (x^2 - y^3)y^l = 0 with l an interger >1. We prove that the boundary of the Milnor fiber is a Waldhausen manifold new in complex geometry, as it cannot be the boundary of a normal surface singularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-04T13:51:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J17",
      "32S25",
      "57M25"
    ],
    "keywords": [
      "milnor fiber",
      "complex surfaces",
      "non-isolated germs",
      "non-reduced plane curve germ",
      "plumbing graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5123M"
    }
  }
}