{
  "abstract": "Let $X$ be a smooth compact irreducible hyperkähler manifold of dimension six. We prove that the second Betti number satisfies $b_2(X) \\le 23$. Furthermore, we show that the third cohomology vanishes whenever $b_2(X) \\ge 19$, and that all odd cohomology vanishes when $b_2(X) = 23$. If the second Chern class lies in the subalgebra generated by $H^2(X,\\mathbb{Q})$, then $b_2(X) \\in \\{5,8,23\\}$. The proof uses the Looijenga--Lunts--Verbitsky decomposition, curvature inequalities for Segre classes, and the Hodge--Riemann bilinear relations on the projective cotangent bundle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15803",
  "author_total": 4,
  "authors": [
    {
      "name": "Jie Fu"
    },
    {
      "name": "Bin Wang"
    },
    {
      "name": "Shihao Wang"
    },
    {
      "name": "Zhiwei Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/33fc3qvrysa48.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15803",
  "fulltext_url": null,
  "id": "33fc3qvrysa48",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15803",
  "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": "W7221754057",
  "pdf_url": "https://arxiv.org/pdf/2610.15803",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/33fc3qvrysa48.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15803",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15803"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Sharp Bound for the Second Betti Number of Hyperkähler Sixfolds",
  "title_text": "A Sharp Bound for the Second Betti Number of Hyperkähler Sixfolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/33fc3qvrysa48",
  "venue": "arXiv",
  "versions": []
}