{
  "id": "1101.5012",
  "version": "v1",
  "published": "2011-01-26T09:34:57.000Z",
  "updated": "2011-01-26T09:34:57.000Z",
  "title": "Invariant theory of foliations of the projective plane",
  "authors": [
    "Eduardo Esteves",
    "Marina Marchisio"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the invariant theory of singular foliations of the projective plane. Our first main result is that a foliation of degree m>1 is not stable only if it has singularities in dimension 1 or contains an isolated singular point with multiplicity at least (m^2-1)/(2m+1). Our second main result is the construction of an invariant map from the space of foliations of degree m to that of curves of degree m^2+m-2. We describe this map explicitly in case m=2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-26T09:34:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariant theory",
      "projective plane",
      "first main result",
      "second main result",
      "isolated singular point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}