{
  "abstract": "We prove that the least common denominator of all genus $g$ Hodge integrals is the Minkowski number $T_{2g}$ or, equivalently, the Bhargava factorial $(2g+1)!_{\\mathbb{P}}$ associated to the set of primes $\\mathbb{P}\\subset\\mathbb{N}$. As a corollary, we prove a conjecture of Liu-Xu on the multiplicity of $3$ in the least common denominators of certain descendant integrals, and generalise their result on a conjecture of Itzykson-Zuber to Hodge integrals with $λ$ classes. Namely, the order of the automorphism group of any pointed stable curve of genus $g'\\le g$ divides the least common denominator of all genus $g$ Hodge integrals. We also comment on the use of generative AI via IMProofBench, which played a fruitful part in the development of this (entirely human-written) paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30274",
  "author_total": 1,
  "authors": [
    {
      "name": "Daniel Holmes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3c38f2kz96dwa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30274",
  "fulltext_url": null,
  "id": "3c38f2kz96dwa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30274",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223329510",
  "pdf_url": "https://arxiv.org/pdf/2610.30274",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3c38f2kz96dwa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30274",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30274"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Denominators of Hodge integrals and Minkowski numbers",
  "title_text": "Denominators of Hodge integrals and Minkowski numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/3c38f2kz96dwa",
  "venue": "arXiv",
  "versions": []
}