{
  "abstract": "We prove the sharp volume bound $\\mathrm{vol}(\\mathcal{F})\\ge 1/6$ for complex foliated surfaces of general type with positive geometric genus. We also study the equality case and apply the bound to the algebraic integrability and finiteness of small volumes on irregular surfaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19788",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhiming Guo"
    },
    {
      "name": "Bokai Hu"
    },
    {
      "name": "Xin Lü"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bankgs7f2w0yy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19788",
  "fulltext_url": null,
  "id": "bankgs7f2w0yy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19788",
  "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|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222022734",
  "pdf_url": "https://arxiv.org/pdf/2610.19788",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bankgs7f2w0yy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19788",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19788"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The volume of foliated surfaces with geometric genus one",
  "title_text": "The volume of foliated surfaces with geometric genus one",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/bankgs7f2w0yy",
  "venue": "arXiv",
  "versions": []
}