{
  "id": "1209.5618",
  "version": "v1",
  "published": "2012-09-25T14:22:39.000Z",
  "updated": "2012-09-25T14:22:39.000Z",
  "title": "Foliations by Curves with Curves as Singularities",
  "authors": [
    "Maurício Corrêa Jr",
    "Arturo Fernandez Perez",
    "Gilcione Nonato Costa",
    "Renato Vidal Martins"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AG",
    "math.CV",
    "math.DS"
  ],
  "abstract": "Let $\\mathcal F$ be a holomorphic one-dimensional foliation on $\\mathbb{P}^n$ such that the components of its singular locus $\\Sigma$ are curves $C_i$ and points $p_j$. We determine the number of $p_j$, counted with multiplicities, in terms of invariants of $\\mathcal F$ and $C_i$, assuming that $\\mathcal F$ is special along the $C_i$. Allowing just one nonzero dimensional component on $\\Sigma$, we also prove results on when the foliation happens to be determined by its singular locus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-25T14:22:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular locus",
      "singularities",
      "holomorphic one-dimensional foliation",
      "nonzero dimensional component",
      "foliation happens"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.5618C"
    }
  }
}