Open Access
July 2015 Automorphisms of open surfaces with irreducible boundary
Adrien Dubouloz, Stéphane Lamy
Osaka J. Math. 52(3): 747-793 (July 2015).


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 Jonquières 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 Jonquières automorphisms, which we call the tame group of $V$, is a proper subgroup of $\mathrm{Aut}(V)$.


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Adrien Dubouloz. Stéphane Lamy. "Automorphisms of open surfaces with irreducible boundary." Osaka J. Math. 52 (3) 747 - 793, July 2015.


Published: July 2015
First available in Project Euclid: 17 July 2015

zbMATH: 1343.14049
MathSciNet: MR3370474

Primary: 14R10
Secondary: 14E30 , 14R25

Rights: Copyright © 2015 Osaka University and Osaka City University, Departments of Mathematics

Vol.52 • No. 3 • July 2015
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