English

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

Group Theory 2024-06-21 v2 Algebraic Geometry Dynamical Systems

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.

Keywords

Cite

@article{arxiv.2307.01334,
  title  = {Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded},
  author = {Anne Lonjou and Piotr Przytycki and Christian Urech},
  journal= {arXiv preprint arXiv:2307.01334},
  year   = {2024}
}

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Minor revisions

R2 v1 2026-06-28T11:21:13.826Z