Rational surfaces with a large group of automorphisms

Cantat, Serge; Dolgachev, Igor

doi:10.1090/S0894-0347-2012-00732-2

Rational surfaces with a large group of automorphisms
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by Serge Cantat and Igor Dolgachev

J. Amer. Math. Soc. 25 (2012), 863-905

DOI: https://doi.org/10.1090/S0894-0347-2012-00732-2

Published electronically: February 23, 2012

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Abstract:

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.

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