{
  "abstract": "Consider a compact leaf $\\mathcal{L}$ of a holomorphic foliation $\\mathcal{F}$ such that all the leaves of the restriction of $\\mathcal{F}$ to some neighborhood $U$ of $\\mathcal{L}$ are closed in $U$. We show that there exists an invariant germ of analytic set $V$ in a neighborhood of $\\mathcal{L}$, of dimension higher than $\\dim (\\mathcal{F})$, consisting of compact leaves, such that the volume of the leaves in $V$ is uniformly bounded by above. We also provide a globalization of this result if the ambient manifold is projective. In order to study closed leaves foliations, and via the holonomy representation, we introduce a new concept, of independent interest, for subgroups $G$ of germs of holomorphic diffeomorphisms, the so called {\\it torsion locus}. We show that it is non-trivial if $G$ has finite orbits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16234",
  "author_total": 1,
  "authors": [
    {
      "name": "Javier Ribón"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/afzkcv1tdgxqj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16234",
  "fulltext_url": null,
  "id": "afzkcv1tdgxqj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16234",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7213423212",
  "pdf_url": "https://arxiv.org/pdf/2609.16234",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/afzkcv1tdgxqj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16234",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16234"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Stability of closed leaves holomorphic foliations via torsion behavior of groups of germs",
  "title_text": "Stability of closed leaves holomorphic foliations via torsion behavior of groups of germs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/afzkcv1tdgxqj",
  "venue": "arXiv",
  "versions": []
}