{
  "id": "2307.01334",
  "version": "v1",
  "published": "2023-07-03T20:13:06.000Z",
  "updated": "2023-07-03T20:13:06.000Z",
  "title": "Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded",
  "authors": [
    "Anne Lonjou",
    "Piotr Przytycki",
    "Christian Urech"
  ],
  "categories": [
    "math.GR",
    "math.AG",
    "math.DS"
  ],
  "abstract": "We prove that any finitely generated subgroup of the plane Cremona group consisting only of algebraic elements is of bounded degree. This follows from a more general result on `decent' actions on infinite direct sums. We apply our results to describe the degree growth of finitely generated subgroups of the plane Cremona group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-03T20:13:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E07",
      "20F65",
      "37F10"
    ],
    "keywords": [
      "finitely generated subgroup",
      "algebraic elements",
      "infinite direct sums",
      "plane cremona group consisting",
      "general result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}