{
  "abstract": "Every singular subalgebroid, and in particular every singular foliation $\\mathscr{G}$, determines a universal Poisson $C^\\infty$-scheme $\\mathrm{Spec}(\\mathcal{F}(\\mathscr{G}))$, which is the analogue of the linear Poisson structure on the dual of a Lie algebroid. We show that the underlying space $X_{\\mathcal{F}(\\mathscr{G})}$ of $\\mathrm{Spec}(\\mathcal{F}(\\mathscr{G}))$ decomposes as a disjoint union of symplectic manifolds. Furthermore, we extend the Helffer-Nourrigat cone to a singular subalgebroid and show that it is an embedded Poisson $C^\\infty$-subscheme of $\\mathrm{Spec}(\\mathcal{F}(\\mathscr{G}))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30395",
  "author_total": 1,
  "authors": [
    {
      "name": "Ruben Louis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/64qhyg11t4a44.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30395",
  "fulltext_url": null,
  "id": "64qhyg11t4a44",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30395",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
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      "arxiv",
      "math.AG"
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      "arxiv",
      "math.DG"
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  "openalex": "W7223308158",
  "pdf_url": "https://arxiv.org/pdf/2610.30395",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/64qhyg11t4a44.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.30395",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30395"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "The symplectic leaves of the affine Poisson $C^\\infty$-scheme associated with a singular subalgebroid",
  "title_text": "The symplectic leaves of the affine Poisson C^∞-scheme associated with a singular subalgebroid",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:45Z",
  "url": "https://research.draconitic.com/paper/64qhyg11t4a44",
  "venue": "arXiv",
  "versions": []
}