{
  "id": "1502.01901",
  "version": "v1",
  "published": "2015-02-06T14:39:15.000Z",
  "updated": "2015-02-06T14:39:15.000Z",
  "title": "On Formal First Integrals for Singularities of Complex Vector Fields",
  "authors": [
    "Jonny Ardila"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1407.4560 by other authors",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that, for a generic germ of foliation of dimension one in $(\\C^3,0)$, the existence of a formal first integral implies the existence of a holomorphic one. This agrees with the same result in other settings obtained in classic works of Mattei&Moussue and Malgrange. Some properties of formal series and formal first integrals are explored.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-06T14:39:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F75",
      "32S65",
      "32M25"
    ],
    "keywords": [
      "complex vector fields",
      "formal first integral implies",
      "singularities",
      "generic germ",
      "classic works"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150201901A"
    }
  }
}