Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups
By Serge Cantat, Keiji Oguiso. 2011
52 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/85b43d5aa2fc51c746391331e8b76284688f7c38
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Automorphism groups of Calabi-Yau manifolds of Picard number two (2012, result): “. The proof for τ∗ 2 is identical. Lemma 6.3. τ−1 i ◦ν : X + i := X → X is the flop of ν i : X → X i and (τ−1 i ◦ν i) −1◦ν i = τ i as birational automorphisms of X. Proof. The proof here is similar to [Og11]. The second statement follows from τ i◦ν i = ν i◦τ i. Therelative Picard numberρ(X/X 1) is 1 ”
- Explicit Examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy (2013, background): “ture in the complex dynamical view. We remark that also for Calabi-Yau manifolds, it seems much harder to construct biregular automorphisms compared with birational selfmaps (See for instance [Og12], [CO12]). On the other hand, our new manifold Y seems so far caught no attention. Now we state the ma”