Rational surfaces with a large group of automorphisms

2011/06/05 by Cantat, Serge, Dolgachev, Igor · 2 citations
#14J26 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1106.0930

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.

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• Compact moduli of elliptic surfaces with a multiple fiber
• Integral Zariski decompositions on smooth projective surfaces II

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