{
  "id": "2409.13520",
  "version": "v1",
  "published": "2024-09-20T14:01:24.000Z",
  "updated": "2024-09-20T14:01:24.000Z",
  "title": "Milnor number of plane curve singularities in arbitrary characteristic",
  "authors": [
    "Enrique Artal Bartolo",
    "Pierrette Cassou-Noguès"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Reduced power series in two variables with coefficients in a field of characteristic zero satisfy a well-known formula that relates a codimension related to the normalization of a ring and the jacobian ideal. In the general case Deligne proved that this formula is only an inequality; Garc\\'ia Barroso and P{\\l}oski stated a conjecture for irreducible power series. In this work we generalize Kouchnirenko's formula for any degenerated power series and also generalize Garc\\'ia Barroso and P{\\l}oski's conjecture. We prove the conjecture in some cases using in particular Greuel and Nguyen.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-20T14:01:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H20",
      "14G17",
      "14B05"
    ],
    "keywords": [
      "plane curve singularities",
      "arbitrary characteristic",
      "milnor number",
      "conjecture",
      "general case deligne"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}