{
  "abstract": "Let $X$ be a smooth projective Poisson surface over an algebraically closed field of characteristic $p>2$, and let $s\\in H^0(X,ω_X^{-1})$ be nonzero. We construct an anticanonical section associated to $s$, called the leafrian, on moduli spaces $M$ of stable objects on $X$, including the moduli of stable sheaves, of principal $G$-bundles, and of instantons. The leafrian splits $M$ if and only if $s^{p-1}$ Frobenius splits the base. It is invariant under the Hamiltonian flows of Bottacin's Poisson structure on $M$, so every compatibly split subvariety of $M$ is a Poisson subvariety. Furthermore, the leafrian extends to an anticanonical section on the Gieseker compactification $\\bar M$, and splits $\\bar M$ under the same criterion. As a consequence, for $X$ a rational surface, a ruled surface over an elliptic curve, a $K3$ surface, or an abelian surface, and $ρ>0$, the Gieseker compactification $\\bar M$ satisfies Kodaira-type cohomology vanishing, including singular $\\bar M$, and the same holds in characteristic zero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31619",
  "author_total": 1,
  "authors": [
    {
      "name": "Jun Peng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e063mfd4bsktn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31619",
  "fulltext_url": null,
  "id": "e063mfd4bsktn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31619",
  "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.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223353347",
  "pdf_url": "https://arxiv.org/pdf/2610.31619",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e063mfd4bsktn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2610.31619",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31619"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Leafrians, Frobenius splittings, and moduli spaces over Poisson surfaces",
  "title_text": "Leafrians, Frobenius splittings, and moduli spaces over Poisson surfaces",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/e063mfd4bsktn",
  "venue": "arXiv",
  "versions": []
}