{
  "abstract": "Given a smooth projective variety $X$ of dimension $n$ and a closed subscheme $Z \\subseteq X$, it is in general a difficult problem to determine whether $X \\setminus Z$ is isomorphic to $\\mathbf A^n$. In the case where $X$ is a projective bundle over $\\mathbf P^1$ and the restriction of every irreducible component of $Z$ to every fibre is a hyperplane, we give a complete geometric characterisation in terms of the irreducible components of $Z$ and their intersections. In the appendix, we use this to obtain a coordinate-free explanation for the recent first counterexample to the Jacobian conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27341",
  "author_total": 1,
  "authors": [
    {
      "name": "Remy van Dobben de Bruyn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1eyzrc3807357.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27341",
  "fulltext_url": null,
  "id": "1eyzrc3807357",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27341",
  "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|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204571411",
  "pdf_url": "https://arxiv.org/pdf/2608.27341",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1eyzrc3807357.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2608.27341",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27341"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Divisors in projective bundles over the projective line whose complement is affine space",
  "title_text": "Divisors in projective bundles over the projective line whose complement is affine space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/1eyzrc3807357",
  "venue": "arXiv",
  "versions": []
}