{
  "abstract": "Levin asked what can be said about the locus of points lying on a given curve in $\\mathbb{G}_m^n$ that have a non-zero integer power on another given curve in $\\mathbb{G}_m^n$ for $n \\geq 3$. We give a definite answer to the abelian analog of Levin's question, proving what is predicted by the Zilber-Pink conjecture in this case. An important ingredient in our proof is a strengthening of a height inequality by Vojta and Rémond.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10212",
  "author_total": 3,
  "authors": [
    {
      "name": "Fabrizio Barroero"
    },
    {
      "name": "Gabriel A. Dill"
    },
    {
      "name": "Lars Kuehne"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/841dq334n1bbg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10212",
  "fulltext_url": null,
  "id": "841dq334n1bbg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10212",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221047106",
  "pdf_url": "https://arxiv.org/pdf/2610.10212",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/841dq334n1bbg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.10212",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10212"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Intersecting a curve in an abelian variety with multiples of another curve",
  "title_text": "Intersecting a curve in an abelian variety with multiples of another curve",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/841dq334n1bbg",
  "venue": "arXiv",
  "versions": []
}