{
  "id": "1811.01189",
  "version": "v1",
  "published": "2018-11-03T10:31:21.000Z",
  "updated": "2018-11-03T10:31:21.000Z",
  "title": "On the number of cusps of deformations of complex polynomials",
  "authors": [
    "Kazumasa Inaba"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AG",
    "math.CV",
    "math.GT"
  ],
  "abstract": "Let f be a 1-variable complex polynomial such that f has a singularity at the origin. In the present paper, we show that there exists a deformation of f which has only fold singularities and cusps as singularities of a real polynomial map from the plane to the plane. We then calculate the number of cusps of a deformation in a sufficiently small neighborhood of the origin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-03T10:31:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R45",
      "58K05",
      "58K60"
    ],
    "keywords": [
      "complex polynomial",
      "deformation",
      "singularity",
      "real polynomial map",
      "sufficiently small neighborhood"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}