Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups

2011/07/29 by Cantat, Serge, Oguiso, Keiji · 1 citation
#14E07 #14E09 #14J32 #14J40 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1107.5862

Abstract

Thanks to the theory of Coxeter groups, we produce the first family of Calabi-Yau manifolds X of arbitrary dimension n, for which \Bir(X) is infinite and the Kawamata-Morrison movable cone conjecture is satisfied. For this family, the movable cone is explicitly described; it's fractal nature is related to limit sets of Kleinian groups and to the Apollonian Gasket. Then, we produce explicit examples of (biregular) automorphisms with positive entropy on some Calabi-Yau manifolds.

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