{
  "id": "2310.16558",
  "version": "v1",
  "published": "2023-10-25T11:23:32.000Z",
  "updated": "2023-10-25T11:23:32.000Z",
  "title": "A multiplicity formula for the Milnor number of smoothable curves",
  "authors": [
    "Andrei Benguş-Lasnier",
    "Terence Gaffney",
    "Antoni Rangachev"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG",
    "math.AC",
    "math.CV"
  ],
  "abstract": "We derive a multiplicity formula for the Milnor number of a reduced smoothable curve singularity generalizing a well-known formula due to L\\^e, Greuel and Teissier for complete intersection curves. We obtain a multiplicity characterization of Whitney equisingularity for families of locally smoothable curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-25T11:23:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S15",
      "32S30",
      "32S60",
      "14C17",
      "13H15"
    ],
    "keywords": [
      "milnor number",
      "multiplicity formula",
      "smoothable curve singularity generalizing",
      "complete intersection curves",
      "whitney equisingularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}