Symétries des surfaces rationelles génériques. (Symmetries of generic rational surfaces) (Q1113966)

We can say that the essential result in this article is that any general rational surface with the Picard number \(r+1\) has no other automorphisms than the identity, if \(r\geq 9.\) To formulate the results, a rational surface \(S_ r\) defined over a large field \(K_ r\) which has transcendence degree 2r-8 over the base field k is considered. It is interesting that the k-automorphism group of \(S_ r\) (not the \(K_ r\)-automorphism group) is isomorphic to the Weyl group \(W_ r\).