{
  "abstract": "Let \\(X\\) be a smooth connected complex projective variety with an effective algebraic \\(\\mathbb C^{\\times}\\)-action, a nonempty finite fixed locus whose weights are \\(\\pm1\\). We show that if its Hattori line bundles are nef, then \\(X\\) is algebraically isomorphic to \\((\\mathbb{P}^1)^{\\dim X}\\), and these bundles become the hyperplane bundles of the factors. The product statement follows from the nef-complexity classification of Enwright and collaborators, and we describe the isomorphism through global sections. To test the required nefness we specialise the orbit-graph criterion of Romano and Wiśniewski. The Hirzebruch surface \\(\\mathbb F_2\\) is an example why the topological hypotheses alone do not imply either the product conclusion or the Fano property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12683",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniel Álvarez"
    },
    {
      "name": "Andrew Clarke"
    },
    {
      "name": "Eduardo González"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1546nnrkgk966.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12683",
  "fulltext_url": null,
  "id": "1546nnrkgk966",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12683",
  "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": "W7221563663",
  "pdf_url": "https://arxiv.org/pdf/2610.12683",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1546nnrkgk966.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12683",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12683"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Nef Hattori classes and products of projective lines",
  "title_text": "Nef Hattori classes and products of projective lines",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/1546nnrkgk966",
  "venue": "arXiv",
  "versions": []
}