Resumen de Distortion in Cremona groups

Serge Cantat, Yves de Cornulier

• 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.