{
  "abstract": "We classify the modular curves $X_0(N)$ that admit a smooth embedding in $\\mathbb P^1 \\times \\mathbb P^1$ and obtain a partial classification for the Shimura curves $X_0^D(N)$. We also prove that, for $D>1$, a Shimura curve $X_0^D(N)$ admits a smooth plane model if and only if its genus is at most one.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13967",
  "author_total": 1,
  "authors": [
    {
      "name": "Oana Padurariu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1y7bh4by0yhez.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13967",
  "fulltext_url": null,
  "id": "1y7bh4by0yhez",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13967",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213251791",
  "pdf_url": "https://arxiv.org/pdf/2609.13967",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1y7bh4by0yhez.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13967",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13967"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Modular and Shimura curves $X_0^D(N)$ embedded in $\\mathbb P^1 \\times \\mathbb P^1$",
  "title_text": "Modular and Shimura curves X_0^D(N) embedded in ℙ^1 × ℙ^1",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/1y7bh4by0yhez",
  "venue": "arXiv",
  "versions": []
}