{
  "abstract": "We find a new presentation of the orbifold fundamental group of the moduli space of cubic surfaces, based on the Artin group of the Petersen graph. This group has two well-known quotients, which appear in the simplest possible way: killing the squares resp. sixth powers of our generators yields the Coxeter group $W(E_6)$ resp. a certain arithmetic group in $\\operatorname{PU}(1,4)$. Along the way we present a certain central extension by $\\mathbb{Z}$, of the genus zero mapping class group with any number of punctures. The $6$-puncture case is essential in this paper, and the general case may have independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16080",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniel Allcock"
    },
    {
      "name": "Tathagata Basak"
    },
    {
      "name": "Eduard Looijenga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/de4sf730gkhaa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16080",
  "fulltext_url": null,
  "id": "de4sf730gkhaa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16080",
  "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|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221834921",
  "pdf_url": "https://arxiv.org/pdf/2610.16080",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/de4sf730gkhaa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16080",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16080"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The moduli space of cubic surfaces and its orbifold fundamental group",
  "title_text": "The moduli space of cubic surfaces and its orbifold fundamental group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/de4sf730gkhaa",
  "venue": "arXiv",
  "versions": []
}