The Jordan constant for Cremona group of rank 2

Abstract

We compute the Jordan constant for the group of birational automorphisms of a projective plane $\mathbb{P}^2_{\mathbb k}$, where ${\mathbb k}$ is either an algebraically closed field of characteristic 0, or the field of real numbers, or the field of rational numbers.Comment: 12 pages, a gap in the proof of Proposition 3.2 removed, some details in the proof of Proposition 3.3 adde