Rational surfaces with a large group of automorphisms
Algebraic Geometry
2012-01-26 v2 Dynamical Systems
Group Theory
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.
Cite
@article{arxiv.1106.0930,
title = {Rational surfaces with a large group of automorphisms},
author = {Serge Cantat and Igor Dolgachev},
journal= {arXiv preprint arXiv:1106.0930},
year = {2012}
}
Comments
48 pages, essentially revised version with corrected proofs, to appear in JAMS