| The discreet part of the automorphism group of the blow-up of N \ge 3 points in the projective plane is a subgroup of the Coxeter group with the Coxeter diagram of type T(2,3,N-3). Examples of surfaces for which this subgroup is of finite index have been known since the beginning of the last century. They are the base points of an Halphen pencil of elliptic curves of degree 9k with 9 k-tuple points, or the set of nodes of a rational plane sextic curve. In my talk I will discuss of a recent result of S. Cantat and myself where we prove that there is nothing else except maybe the set of torsion points on a plane cubic. |