{
  "abstract": "The Albanese fibration of the Cartwright--Steger surface is a genus-$19$ Lefschetz fibration over a torus. We give an explicit formula for it: in the projective model of Borisov and Yeung, the map is represented by three homogeneous polynomials of degree $13$ with integer coefficients, and its target is the elliptic curve $Y^2Z=X^3-3888Z^3$. A recognition theorem shows that it suffices to verify one polynomial identity on the surface. A coefficient bound allows us to establish the identity over $Q$ from computations modulo primes. We also determine exact coordinates for the three nodes and their images on the elliptic curve.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23124",
  "author_total": 1,
  "authors": [
    {
      "name": "Zoltán Szabó"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ds3x17e72ywg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23124",
  "fulltext_url": null,
  "id": "8ds3x17e72ywg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23124",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214000598",
  "pdf_url": "https://arxiv.org/pdf/2609.23124",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ds3x17e72ywg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23124",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23124"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A polynomial formula for the Albanese map of the Cartwright-Steger surface",
  "title_text": "A polynomial formula for the Albanese map of the Cartwright-Steger surface",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/8ds3x17e72ywg",
  "venue": "arXiv",
  "versions": []
}