AUTOMORPHISMS OF OPEN SURFACES WITH IRREDUCIBLE BOUNDARY

Let (S, B-S) be the log pair associated with a projective completion of a smooth quasi-projective surface V. Under the assumption that the boundary B-S is irreducible, we obtain an algorithm to factorize any automorphism of V into a sequence of simple links. This factorization lies in the framework of the log Mori theory, with the property that all the blow-ups and contractions involved in the process occur on the boundary. When the completion S is smooth, we obtain a description of the automorphisms of V which is reminiscent of a presentation by generators and relations except that the ``generators'' are no longer automorphisms. They are instead isomorphisms between different models of V preserving certain rational fibrations. This description enables one to define normal forms of automorphisms and leads in particular to a natural generalization of the usual notions of affine and Jonquieres automorphisms of the affine plane. When V is affine, we show however that except for a finite family of surfaces including the affine plane, the group generated by these affine and JonquiSres automorphisms, which we call the tame group of V, is a proper subgroup of Aut(V).