{
  "id": "1106.1191",
  "version": "v1",
  "published": "2011-06-06T20:21:36.000Z",
  "updated": "2011-06-06T20:21:36.000Z",
  "title": "Specialization to the tangent cone and Whitney Equisingularity",
  "authors": [
    "Arturo Giles Flores"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let (X,0) be a reduced, equidimensional germ of analytic singularity with reduced tangent cone (C_{X,0},0). We prove that the absence of exceptional cones is a necessary and sufficient condition for the smooth part \\X^0 of the specialization to the tangent cone \\phi: \\X \\to \\C to satisfy Whitney's conditions along the parameter axis Y. This result is a first step in generalizing to higher dimensions L\\^e and Teissier's result for hypersurfaces of \\C^3 which establishes the Whitney equisingularity of X and its tangent cone under this conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-06T20:21:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J17",
      "32S15"
    ],
    "keywords": [
      "whitney equisingularity",
      "specialization",
      "satisfy whitneys conditions",
      "smooth part",
      "reduced tangent cone"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.1191F"
    }
  }
}