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

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.

30 pages. Though the most main theorem is the same, many explanations and results are polished up or made stronger. Theorem 4.6 (based on section 2.2) is not in the previous version. A version with figure is in http://perso.univ-rennes1.fr/serge.cantat/