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

2023/07/03 by Anne Lonjou, Lonjou, Anne, Piotr Przytycki +3
Mathematics · #14E07 #20F65 #37F10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.2307.01334

openalex publication_date 2023/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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