{
  "id": "1611.03800",
  "version": "v1",
  "published": "2016-11-11T17:57:40.000Z",
  "updated": "2016-11-11T17:57:40.000Z",
  "title": "On the geometry of the singular locus of a codimension one foliation in $\\mathbb{P}^n$",
  "authors": [
    "Omegar Calvo-Andrade",
    "Ariel Molinuevo",
    "Federico Quallbrunn"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We will work with codimension one holomorphic foliations over the complex projective space, represented by integrable forms $\\omega\\in H^0(\\Omega^1_{\\mathbb{P}^n}(e))$. Our main result is that, under suitable hypotheses, the Kupka set of the singular locus of $\\omega$, defined algebraically as a scheme, turns out to be arithmetically Cohen-Macaulay. As a consequence, we prove the connectedness of the Kupka set, and the splitting of the tangent sheaf of the foliation, provided that it is locally free.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-11T17:57:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular locus",
      "codimension",
      "kupka set",
      "main result",
      "holomorphic foliations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}