[Les sous-groupes de type fini d’éléments algébriques du groupe de Cremona planaire sont bornés]
Nous montrons que tout sous-groupe de type fini du groupe de Cremona planaire contenant seulement des éléments algébriques est de degré borné. Cela découle d’un résultat plus général sur les actions « décentes » sur les produits infinis restreints. Nous appliquons nos résultats pour décrire la croissance des degrés des sous-groupes de type fini du groupe de Cremona planaire.
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 restricted products. We apply our results to describe the degree growth of finitely generated subgroups of the plane Cremona group.
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Keywords: Cremona group, algebraic elements, locally elliptic actions, degree growth
Mot clés : Groupe de Cremona, éléments algébriques, actions purement elliptiques, croissance des degrés
Anne Lonjou 1 ; Piotr Przytycki 2 ; Christian Urech 3
CC-BY 4.0
@article{JEP_2024__11__1011_0,
author = {Anne Lonjou and Piotr Przytycki and Christian Urech},
title = {Finitely generated subgroups of algebraic~elements of plane {Cremona} groups are~bounded},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {1011--1028},
publisher = {\'Ecole polytechnique},
volume = {11},
year = {2024},
doi = {10.5802/jep.271},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.271/}
}
TY - JOUR AU - Anne Lonjou AU - Piotr Przytycki AU - Christian Urech TI - Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded JO - Journal de l’École polytechnique — Mathématiques PY - 2024 SP - 1011 EP - 1028 VL - 11 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.271/ DO - 10.5802/jep.271 LA - en ID - JEP_2024__11__1011_0 ER -
%0 Journal Article %A Anne Lonjou %A Piotr Przytycki %A Christian Urech %T Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded %J Journal de l’École polytechnique — Mathématiques %D 2024 %P 1011-1028 %V 11 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.271/ %R 10.5802/jep.271 %G en %F JEP_2024__11__1011_0
Anne Lonjou; Piotr Przytycki; Christian Urech. Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded. Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 1011-1028. doi : 10.5802/jep.271. https://jep.centre-mersenne.org/articles/10.5802/jep.271/
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