{
  "abstract": "We prove that a singular Hermitian metric $h$ on a vector bundle agrees almost everywhere with a Griffiths semipositive metric if its dual metric $h^*$ is locally integrable and the $\\bar \\partial$-equation admits solutions with optimal $L^2$-estimates for $(n,n)$-forms, where $n$ is the dimension of the base manifold. In particular, under this integrability assumption, Nakano semipositivity in the sense of optimal estimates implies Griffiths semipositivity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25900",
  "author_total": 1,
  "authors": [
    {
      "name": "Shin-ichi Matsumura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74hrm25kxt61d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25900",
  "fulltext_url": null,
  "id": "74hrm25kxt61d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25900",
  "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.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7223029397",
  "pdf_url": "https://arxiv.org/pdf/2610.25900",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74hrm25kxt61d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25900",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25900"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A characterization of Griffiths semipositivity by top-degree optimal $\\bar \\partial$-estimates",
  "title_text": "A characterization of Griffiths semipositivity by top-degree optimal ∂̅-estimates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/74hrm25kxt61d",
  "venue": "arXiv",
  "versions": []
}