Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded (Q6621560)

In the paper under review, the authors showed that a finitely generated subgroup of the plane Cremona group whose elements all have bounded degree growth is a bounded and algebraic subgroup of the Cremona group. This answers a question of Cantat and Favre a decade ago.\N\NThe first and the third author [Duke Math. J. 170, No. 17, 3703--3743 (2021; Zbl 1493.14016)] constructed previously a cube complex on which the plane Cremona acts. This is the main tool for the authors' proof. Note that by a result of \textit{S. Cantat} [Ann. Math. (2) 174, No. 1, 299--340 (2011; Zbl 1233.14011)], for the purpose of the paper under review, it suffices to restrict to a subcomplex of the cube complex corresponding to de Jonquières maps.