{
  "abstract": "We prove the following two statements: (1) If $X$ is a compact Kähler fourfold with pseudo-effective canonical bundle and no subvarieties of codimension one or two, then $K_X$ is a torsion line bundle; (2) If $X$ is a compact Kähler fourfold with no subvarieties of codimension one or two, then $X$ is not uniruled. Using the Beauville-Bogomolov decomposition and a characterization of Uniruled manifolds by Wenhao Ou, we get that if $X$ is a compact Kähler fourfold with no subvarieties of codimension one or two, then either $X$ is a torus or an irreducible holomorphic symplectic manifold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.04536",
  "author_total": 1,
  "authors": [
    {
      "name": "Pisya Vikash"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9x28phpsnx0r1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.04536",
  "fulltext_url": null,
  "id": "9x28phpsnx0r1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.04536",
  "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"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7167642616",
  "pdf_url": "https://arxiv.org/pdf/2607.04536",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9x28phpsnx0r1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2607.04536",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.04536"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Classification of Smooth Minimal Kähler Fourfolds Without Effective Divisors and Surfaces",
  "title_text": "Classification of Smooth Minimal Kähler Fourfolds Without Effective Divisors and Surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/9x28phpsnx0r1",
  "venue": "arXiv",
  "versions": []
}