{
  "abstract": "Let $\\mathcal G$ be a split semiabelian variety of dimension $n \\ge 2$ and let $\\mathcal C \\subset \\mathcal G$ an irreducible curve, where everything is defined over $\\overline{\\mathbb{Q}}$. We prove that, under the natural hypothesis that $\\mathcal C$ is not contained in any proper algebraic subgroup of $\\mathcal G$, the set of points $P$ of $\\mathcal C$ lying in an algebraic subgroup $H$ which intersects the curve tangentially at $P$ is finite. This generalizes a result for curves in 2-dimensional tori by Marché and Maurin. We apply these results to square-freeness of certain geometric divisibility sequences.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35307",
  "author_total": 3,
  "authors": [
    {
      "name": "Francesco Ballini"
    },
    {
      "name": "Laura Capuano"
    },
    {
      "name": "Nicola Ottolini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8h6hd36zc271w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35307",
  "fulltext_url": null,
  "id": "8h6hd36zc271w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35307",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214748514",
  "pdf_url": "https://arxiv.org/pdf/2609.35307",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8h6hd36zc271w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35307",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35307"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Singular intersections in split semiabelian varieties",
  "title_text": "Singular intersections in split semiabelian varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/8h6hd36zc271w",
  "venue": "arXiv",
  "versions": []
}