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Article Dans Une Revue American Journal of Mathematics Année : 2015

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

Serge Cantat
Keiji Oguiso
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Résumé

Dedicated to Professor Yujiro Kawamata on the occasion of his sixtieth birthday. 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 Calaby-Yau varieties.
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Dates et versions

hal-02328055 , version 1 (23-10-2019)

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Serge Cantat, Keiji Oguiso. Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups. American Journal of Mathematics, 2015, 137 (4), pp.1013-1044. ⟨10.1353/ajm.2015.0023⟩. ⟨hal-02328055⟩
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