{
  "id": "math/0011205",
  "version": "v1",
  "published": "2000-11-24T00:42:32.000Z",
  "updated": "2000-11-24T00:42:32.000Z",
  "title": "Vector Fields, Invariant Varieties and Linear Systems",
  "authors": [
    "Jorge Vitorio Pereira"
  ],
  "comment": "15 pages, Latex",
  "journal": "Annales de L'Institut Fourier, 51 no.5, pp.1385-1405, 2001.",
  "categories": [
    "math.DS",
    "math.AG"
  ],
  "abstract": "We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of such investigation we obtain a computational criteria for the existence of rational first integrals of a given degree, bounds for the number of first integrals on families of vector fields and a generalization of Darboux's criteria. We also provide a new proof of Gomez-Mont's result on foliations with all leaves algebraic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-11-24T00:42:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vector field",
      "invariant varieties",
      "linear systems",
      "rational first integrals",
      "inflection locus"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....11205V"
    }
  }
}