{
  "id": "2401.07015",
  "version": "v1",
  "published": "2024-01-13T08:51:05.000Z",
  "updated": "2024-01-13T08:51:05.000Z",
  "title": "Finite translation orbits on double families of abelian varieties",
  "authors": [
    "Paolo Dolce",
    "Francesco Tropeano"
  ],
  "comment": "20 pages, 2 figures. Comments are welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Consider two distinct families of $g$-dimensional abelian varieties with the same domain $\\mathcal A$ and codomain $S$, and both endowed with a non-torsion section. Such sections induce two fiberwise translations on $\\mathcal A$. We show that if $\\dim S\\le g$, the points with finite orbit under the action of a certain subset of the group generated by both translations lie in a proper Zariski closed subset that can be described to a certain extent. Our work is a higher dimensional generalization of a result of Corvaja, Tsimermann and Zannier.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-13T08:51:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14Gxx",
      "14Kxx",
      "11G10"
    ],
    "keywords": [
      "finite translation orbits",
      "double families",
      "dimensional abelian varieties",
      "proper zariski closed subset",
      "higher dimensional generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}