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

View

Related Concepts

Coxeter group Mathematics Calabi–Yau manifold Automorphism Conjecture Cone (formal languages) Pure mathematics Coxeter complex Type (biology) Dimension (graph theory) Coxeter element Combinatorics Artin group Algorithm Ecology Biology

Serge Cantat , Keiji Oguiso ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.1353/ajm.2015.0023 · OA: W2171480931

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.