{
  "id": "1305.5102",
  "version": "v1",
  "published": "2013-05-22T12:23:13.000Z",
  "updated": "2013-05-22T12:23:13.000Z",
  "title": "A bound for the Milnor number of plane curve singularities",
  "authors": [
    "Arkadiusz Płoski"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $f=0$ be a plane algebraic curve of degree $d>1$ with an isolated singular point at the origin of the complex plane. We show that the Milnor number $\\mu_0(f)$ is less than or equal to $(d-1)^2-\\left[\\frac{d}{2}\\right]$, unless $f=0$ is a set of $d$ concurrent lines passing through 0. Then we characterize the curves $f=0$ for which $\\mu_0(f)=(d-1)^2-\\left[\\frac{d}{2}\\right]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-22T12:23:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "plane curve singularities",
      "milnor number",
      "plane algebraic curve",
      "isolated singular point",
      "complex plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.5102P"
    }
  }
}