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