Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded

Anne Lonjou, Piotr Przytycki, Christian Urech

Published 2023-07-03Version 1

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.