{
  "id": "2301.10313",
  "version": "v1",
  "published": "2023-01-24T21:29:18.000Z",
  "updated": "2023-01-24T21:29:18.000Z",
  "title": "Singularities of holomorphic codimension one foliations of the complex projective plane",
  "authors": [
    "Dominique Cerveau",
    "Julie Déserti"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that any holomorphic codimension 1 foliation on the complex projective plane has at most one singular point up to the action of an ad-hoc birational self map of the complex projective plane into itself. Consequently, any algebraic foliation on the affine plane has no singularities up to the action of a suitable birational self map of the complex projective plane into itself.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-24T21:29:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S65"
    ],
    "keywords": [
      "complex projective plane",
      "holomorphic codimension",
      "singularities",
      "ad-hoc birational self map",
      "suitable birational self map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}