{
  "id": "math/0309322",
  "version": "v1",
  "published": "2003-09-19T12:50:58.000Z",
  "updated": "2003-09-19T12:50:58.000Z",
  "title": "Computation of Milnor numbers and critical values at infinity",
  "authors": [
    "Arnaud Bodin"
  ],
  "comment": "9 pages.To download the libraries for Singular see http://www-gat.univ-lille1.fr/~bodin/",
  "journal": "Journal of Symbolic Computation (2004, vol. 38, 1417-1427)",
  "doi": "10.1016/j.jsc.2004.04.003",
  "categories": [
    "math.AG",
    "math.GT"
  ],
  "abstract": "We describe how to compute topological objects associated to a polynomial map of several complex variables with isolated singularities. These objects are: the affine critical values, the affine Milnor numbers for all irregular fibers, the critical values at infinity, and the Milnor numbers at infinity for all irregular fibers. Then for a family of polynomials we detect parameters where the topology of the polynomials can change. Implementation and examples are given with the computer algebra system Singular.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-19T12:50:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "computation",
      "computer algebra system singular",
      "irregular fibers",
      "affine milnor numbers",
      "detect parameters"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9322B"
    }
  }
}