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Rational surfaces with a large group of automorphisms

2012; American Mathematical Society; Volume: 25; Issue: 3 Linguagem: Inglês

10.1090/s0894-0347-2012-00732-2

1088-6834

Serge Cantat, Igor Dolgachev,

Mathematical Dynamics and Fractals

We classify rational surfaces $X$ for which the image of the automorphism group $\mathrm {Aut}(X)$ in the group of linear transformations of the Picard group $\mathrm {Pic}(X)$ is the largest possible. This answers a question raised by Arthur Coble in 1928, and can be rephrased in terms of periodic orbits of birational actions of infinite Coxeter groups.