{
  "abstract": "We give a geometric proof of the following statement: let $X$ be a smooth hyperkähler fourfold such that the Picard group is generated by a line bundle $L$ that is nef, non-trivial, and not big. If the Kodaira dimension of $L$ is non-negative, some positive multiple defines a Lagrangian fibration. The proof requires a number of tools which are of independent interest, including an analogue of Voisin's unobstructedness result and a smoothing result for singular Lagrangian subvarieties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31497",
  "author_total": 3,
  "authors": [
    {
      "name": "Andreas Höring"
    },
    {
      "name": "Vladimir Lazić"
    },
    {
      "name": "Christian Lehn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f949h86gmmks6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31497",
  "fulltext_url": null,
  "id": "f949h86gmmks6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31497",
  "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.DG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223355124",
  "pdf_url": "https://arxiv.org/pdf/2610.31497",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f949h86gmmks6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31497",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31497"
    }
  ],
  "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.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A semiampleness result for hyperkähler fourfolds and smoothings of Lagrangian subvarieties",
  "title_text": "A semiampleness result for hyperkähler fourfolds and smoothings of Lagrangian subvarieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/f949h86gmmks6",
  "venue": "arXiv",
  "versions": []
}