{
  "id": "2201.07479",
  "version": "v1",
  "published": "2022-01-19T09:08:17.000Z",
  "updated": "2022-01-19T09:08:17.000Z",
  "title": "Topological Moduli Space for Germs of Holomorphic Foliations III: Complete families",
  "authors": [
    "David Marín",
    "Jean-François Mattei",
    "Éliane Salem"
  ],
  "comment": "The paper entitled \"Topologically complete families of germs of holomorphic foliations\" with reference arXiv:2105.12688 (version 1) has been modified and divided in two parts: the paper \"Topological moduli space for germs of holomorphic foliations II: Universal deformations\" with reference arXiv:2105.12688v2 and the current paper",
  "categories": [
    "math.DS",
    "math.CA",
    "math.CV"
  ],
  "abstract": "In this work we use our previous results on the topological classification of generic singular foliation germs on $(\\mathbb C^{2},0)$ to construct complete families: after fixing the semi-local topological invariants we prove the existence of a minimal family of foliation germs that contain all the topological classes and such that any equisingular global family with parameter space an arbitrary complex manifold factorizes through it.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-19T09:08:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F75",
      "32M25",
      "32S50",
      "32S65"
    ],
    "keywords": [
      "topological moduli space",
      "holomorphic foliations",
      "arbitrary complex manifold factorizes",
      "generic singular foliation germs",
      "construct complete families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}