Rational surfaces with a large group of automorphisms

Details Rational surfaces with a large group of automorphisms Rational surfaces with a large group of automorphisms

2011-06-05

arxiv.org/abs/1106.0930v2

Mathematics

Algebraic Geometry

48 pages, essentially revised version with corrected proofs, to appear in JAMS

Scientific paper

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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