{
  "abstract": "Building on an earlier classification of smooth weak Fano threefolds of Picard number two with small anticanonical morphism, we prove that Case~28 of the table of E1-E1 links from that classification is geometrically realizable. We construct the link by blowing up a smooth rational cubic curve on a degree-two del Pezzo threefold $V_2$, realized as a quartic double solid. A lattice calculation on an anticanonical K3 surface shows that the anticanonical morphism of the blow-up is small, and the covering involution of the anticanonical double cover realizes the flop. The resulting Sarkisov link is a birational involution with the numerical invariants of E1-E1 Case~28.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26364",
  "author_total": 2,
  "authors": [
    {
      "name": "Joseph Cutrone"
    },
    {
      "name": "Nicholas Marshburn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6k456drrwp89j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26364",
  "fulltext_url": null,
  "id": "6k456drrwp89j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26364",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223003424",
  "pdf_url": "https://arxiv.org/pdf/2610.26364",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6k456drrwp89j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26364",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26364"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Sarkisov Involution from a Rational Cubic Curve on a Quartic Double Solid",
  "title_text": "A Sarkisov Involution from a Rational Cubic Curve on a Quartic Double Solid",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/6k456drrwp89j",
  "venue": "arXiv",
  "versions": []
}