{
  "abstract": "We classify commensurability relations between Deligne--Mostow--Thurston monodromy groups and the sixteen arithmetic Ghazouani--Pirio monodromy groups arising from moduli of flat cone metrics on the sphere and on the torus. In both settings, the monodromy group preserves a skew-Hermitian form coming from twisted homology. We use a degeneration method to compute their determinant classes in the genus one case. The defining CM fields and determinant classes of the skew-Hermitian forms determine the commensurability relations. In particular, each of the sixteen arithmetic Ghazouani--Pirio monodromy groups is commensurable with an arithmetic Deligne--Mostow--Thurston monodromy group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11482",
  "author_total": 2,
  "authors": [
    {
      "name": "Chenglong Yu"
    },
    {
      "name": "Yiming Zhong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f71bhjhrp656e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11482",
  "fulltext_url": null,
  "id": "f71bhjhrp656e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11482",
  "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.GT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7212275207",
  "pdf_url": "https://arxiv.org/pdf/2609.11482",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f71bhjhrp656e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11482",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11482"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Commensurability Relations Between Deligne-Mostow-Thurston and Ghazouani-Pirio Monodromy Groups",
  "title_text": "Commensurability Relations Between Deligne-Mostow-Thurston and Ghazouani-Pirio Monodromy Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/f71bhjhrp656e",
  "venue": "arXiv",
  "versions": []
}