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arXiv · 1106.0930

Rational surfaces with a large group of automorphisms

Serge Cantat·Igor Dolgachev
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Abstract

We classify rational surfaces for which the image of the automorphisms group in the group of linear transformations of the Picard group is the largest possible. This answers a question raised by Arthur Coble in 1928, and can be rephrased in terms of periodic orbits of a birational action of an infinite Coxeter group on ordered point sets in the projective plane modulo projective equivalence. We also outline the classification of non-rational surfaces with large automorphism groups.

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Serge Cantat, Igor Dolgachev. 2012-01-25. Rational surfaces with a large group of automorphisms. https://arxiv.org/abs/1106.0930

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