{
  "abstract": "We consider smooth proper families of compact complex manifolds over a disk whose total space is Kähler, together with a boundary divisor with relative simple normal crossings. We prove that, if the boundary is a rational divisor with coefficients in $[0,1)$, every logarithmic pluricanonical form on a fiber extends to a neighborhood of that fiber, and hence that the logarithmic plurigenera are constant. No positivity of the log canonical class is assumed. We prove further that, for real boundary coefficients in $[0,1]$, a log-adjoint class twisted by a smooth semipositive form has the same volume on every fiber, and that it is pseudoeffective either on every fiber or on none. When the log-adjoint class is nef on every fiber, we give a second proof of the extension theorem, which does not use the minimal model program.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26519",
  "author_total": 2,
  "authors": [
    {
      "name": "Kefeng Liu"
    },
    {
      "name": "Xueyuan Wan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aq8jafj3c7pns.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26519",
  "fulltext_url": null,
  "id": "aq8jafj3c7pns",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26519",
  "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"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7223041585",
  "pdf_url": "https://arxiv.org/pdf/2610.26519",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aq8jafj3c7pns.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26519",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26519"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Invariance of logarithmic plurigenera and adjoint volumes in Kähler families",
  "title_text": "Invariance of logarithmic plurigenera and adjoint volumes in Kähler families",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/aq8jafj3c7pns",
  "venue": "arXiv",
  "versions": []
}