{
  "abstract": "In 1986, Deligne and Mostow constructed a ball quotient $\\mathbb{B}^2 / Γ$ biholomorphic to the complex projective plane $\\mathbb{P}^2$ whose branch locus is a line arrangement. In this paper, we show that if $\\mathbb{P}^2$ is realized as a ball quotient whose branch divisor $D$ is an arrangement of smooth pairwise normal-crossing curves, then the orbifold $(\\mathbb{P}^2,D)$ is isomorphic to either the Deligne-Mostow example or a certain degree 9 cover of it. This classification of \"ball quotient structures\" on $\\mathbb{P}^2$ generalizes the $\\mathbb{P}^1$ case due to Poincaré.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.18710",
  "author_total": 1,
  "authors": [
    {
      "name": "Cindy Tan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1pg8phxhak802.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.18710",
  "fulltext_url": null,
  "id": "1pg8phxhak802",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.18710",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  ],
  "openalex": "W7170091130",
  "pdf_url": "https://arxiv.org/pdf/2607.18710",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1pg8phxhak802.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2607.18710",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.18710"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The complex projective plane as a ball quotient",
  "title_text": "The complex projective plane as a ball quotient",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/1pg8phxhak802",
  "venue": "arXiv",
  "versions": []
}