Rational surfaces with a large group of automorphisms

Serge Cantat (1) , Igor Dolgachev (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Mathematics

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.

Domaines: Géométrie algébrique [math.AG]; Systèmes dynamiques [math.DS]; Théorie des groupes [math.GR]

Serge Cantat, Igor Dolgachev. Rational surfaces with a large group of automorphisms. Journal of the American Mathematical Society, 2012, 25 (3), pp.863-905. ⟨10.1090/S0894-0347-2012-00732-2⟩. ⟨hal-00705290⟩