Distortion in Cremona groups

• Serge Cantat ^[2] ; Yves De Cornulier ^[1]
  1. [1] Claude Bernard University Lyon 1

     Claude Bernard University Lyon 1

     Arrondissement de Lyon, Francia

     
  2. [2] Université Rennes, France
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 20, Nº 2, 2020, págs. 827-858
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We study the distortion of elements in two-dimensional Cremona groups over algebraically closed fields of characteristic zero. We obtain the following trichotomy: non-elliptic elements (i.e., those whose powers have unbounded degree) are undistorted, and elliptic elements have a doubly exponential distortion when they are virtually unipotent or an exponential distortion otherwise.