{
  "id": "math/0002052",
  "version": "v1",
  "published": "2000-02-07T18:16:29.000Z",
  "updated": "2000-02-07T18:16:29.000Z",
  "title": "The Alexander polynomial of a plane curve singularity and the ring of functions on it",
  "authors": [
    "A. Campillo",
    "F. Delgado",
    "S. M. Gusein-Zade"
  ],
  "comment": "5 pages, LaTeX",
  "categories": [
    "math.AG",
    "math.GT"
  ],
  "abstract": "We give two formulae which express the Alexander polynomial $\\Delta^C$ of several variables of a plane curve singularity $C$ in terms of the ring ${\\cal O}_{C}$ of germs of analytic functions on the curve. One of them expresses $\\Delta^C$ in terms of dimensions of some factorspaces corresponding to a (multi-indexed) filtration on the ring ${\\cal O}_{C}$. The other one gives the coefficients of the Alexander polynomial $\\Delta^C$ as Euler characteristics of some explicitly described spaces (complements to arrangements of projective hyperplanes).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-02-07T18:16:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S05",
      "14H20"
    ],
    "keywords": [
      "plane curve singularity",
      "alexander polynomial",
      "analytic functions",
      "euler characteristics",
      "hyperplanes"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......2052C"
    }
  }
}