Rational surfaces with a large group of automorphisms

By Serge Cantat, Igor Dolgachev. 2011

90 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5e289d43ff98faec247f854b61730d66b8ba6ebc

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Dynamics of automorphisms of compact complex surfaces (2014, methodology): “We refer to [80, 7, 9, 102] for constructions of examples, to [8, 48] for their deformations, and to [31] for restrictions on the size of such groups of automorphisms.”
Normal subgroups in the Cremona group (2010, background): “A proof is sketched in [24, 23], and a complete, characteristic free, proof is available in [7]; analogous result and proof for generic Enriques surfaces can be found in [21].”
Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups (2011, background): “r a simplex. 1.2. Wehler varieties. Coxeter groups also appear in the theory of algebraic surfaces, mostly as hyperbolic reﬂection groups acting on N éron-Severi groups (see for instance [Ni], [Bor], [CaDo], [Do], [Mc2], [To]). Let n be a positive integer. Let X be a smooth complex hypersurface of (”