{
  "abstract": "Let $X$ be a complex $\\mathbb Q$-factorial Gorenstein Fano fourfold with $ρ(X)=1$. If $X$ has canonical singularities, we prove that $(-K_X)^4\\le3528$, with equality if and only if $(X\\simeq \\mathbb P(1,1,12,28,42)$. In fact, $(-K_X)^4\\ge3130$ already implies this isomorphism. If $X$ has terminal singularities, we prove the sharp bound $(-K_X)^4\\le648$, with equality if and only if $X\\simeq \\mathbb P(1,1,1,1,2)$. In the canonical case, we also obtain the sharp bound $(-K_X)^4\\le1024$ when a positive generator of $Cl(X)/ \\mathrm{tors}$ is Cartier outside a finite set. The proofs use jet estimates involving all Harder--Narasimhan slopes of the tangent sheaf, the geometry of algebraic foliations, and the integrality of intersection numbers on a general leaf. The equality case in the canonical bound is determined by two computations of divisorial section rings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09419",
  "author_total": 2,
  "authors": [
    {
      "name": "Pinxian Bie"
    },
    {
      "name": "Zhengjie Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/av0rj0vwea8vp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09419",
  "fulltext_url": null,
  "id": "av0rj0vwea8vp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09419",
  "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": "W7220895027",
  "pdf_url": "https://arxiv.org/pdf/2610.09419",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/av0rj0vwea8vp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.09419",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09419"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Sharp anticanonical volume bounds for Gorenstein Fano fourfold of Picard number one",
  "title_text": "Sharp anticanonical volume bounds for Gorenstein Fano fourfold of Picard number one",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/av0rj0vwea8vp",
  "venue": "arXiv",
  "versions": []
}