{
  "abstract": "We study the geometry of Shimura varieties associated with a Hermitian form of signature $(p,q)$ over an imaginary quadratic field $E$, where $2\\leq p\\leq q$. We prove that when $p\\geq w_E$ and $(p,q)\\neq(2,2),(2,3)$, where $w_E:=\\#\\mathscr{O}_E^\\times$, there exists a toroidal compactification with at worst canonical singularities. As an application, combining this singularity analysis with Arthur's multiplicity formula, we prove that only finitely many pairs $(p,q)$ satisfying the above conditions and $p+q\\equiv1\\pmod{w_E}$ give rise to unitary Shimura varieties that are not of general type. Our method also improves the singularity bound of Gritsenko--Hulek--Sankaran (Invent.\\ Math., 2007) for $\\mathrm{O}^+(2,n)$ to the range $n\\geq6$ and shows that this bound is sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18146",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuji Horinaga"
    },
    {
      "name": "Yota Maeda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a16280ng23xdz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18146",
  "fulltext_url": null,
  "id": "a16280ng23xdz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18146",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7213506208",
  "pdf_url": "https://arxiv.org/pdf/2609.18146",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a16280ng23xdz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18146",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18146"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the singularities and the Kodaira dimension of unitary Shimura varieties",
  "title_text": "On the singularities and the Kodaira dimension of unitary Shimura varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/a16280ng23xdz",
  "venue": "arXiv",
  "versions": []
}