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Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 137, Number 4, August 2015
- pp. 1013-1044
- 10.1353/ajm.2015.0023
- Article
- Additional Information
Thanks to the theory of Coxeter groups, we produce the first family of Calabi-Yau manifolds $X$ of arbitrary
dimension $n$, for which ${\rm Bir}(X)$ 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 varieties.