{
  "id": "2309.13730",
  "version": "v1",
  "published": "2023-09-24T19:20:46.000Z",
  "updated": "2023-09-24T19:20:46.000Z",
  "title": "Families of automorphisms of abelian varieties",
  "authors": [
    "Charles Favre",
    "Alexandra Kuznetsova"
  ],
  "comment": "34 pages, 2 tables",
  "categories": [
    "math.AG",
    "math.DS"
  ],
  "abstract": "We consider some algebraic aspects of the dynamics of an automorphism on a family of polarized abelian varieties parameterized by the complex unit disk. When the action on the cohomology of the generic fiber has no cyclotomic factor, we prove that such a map can be made regular only if the family of abelian varieties does not degenerate. As a contrast, we show that families of translations are always regularizable. We further describe the closure of the orbits of such maps, inspired by results of Cantat and Amerik-Verbitsky.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-24T19:20:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J50",
      "14K22",
      "32H50"
    ],
    "keywords": [
      "automorphism",
      "complex unit disk",
      "algebraic aspects",
      "polarized abelian varieties",
      "generic fiber"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}