{
  "id": "2309.07829",
  "version": "v1",
  "published": "2023-09-14T16:19:20.000Z",
  "updated": "2023-09-14T16:19:20.000Z",
  "title": "Minimality of the $\\mathcal D$-groupoid of symmetries of a projective structure",
  "authors": [
    "Alejandro Arenas Tirado",
    "David Blázquez-Sanz",
    "Guy Casale"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AG",
    "math.DG",
    "math.LO"
  ],
  "abstract": "In this article we study Kummer's $\\mathcal D$-groupoid, which is the groupoid of symmetries of a meromorphic projective structure. We give necessary and sufficient conditions for its minimality, in the sense of not having infinite sub-$\\mathcal D$-groupoids. The condition that we find turns out to be equivalent to the strong minimality of the non-linear Schwarzian equation and the non-integrability by means of Liouvillian functions of the linear Schwarzian equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-14T16:19:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34M15",
      "03C50"
    ],
    "keywords": [
      "symmetries",
      "non-linear schwarzian equation",
      "strong minimality",
      "sufficient conditions",
      "study kummers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}