Conjugacy classes of affine automorphisms of and linear automorphisms of ℙn in the Cremona groups

Abstract

We describe the conjugacy classes of affine automorphisms in the group $Aut(n,\K)$ (respectively $Bir(\K^n)$) of automorphisms (respectively of birational maps) of $\K^n$. From this we deduce also the classification of conjugacy classes of automorphisms of $\Pn$ in the Cremona group $Bir(\K^n)$.