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

TL;DR

This paper constructs new Calabi-Yau manifolds of any dimension with infinite birational automorphism groups, satisfying the movable cone conjecture, and explores their automorphisms and fractal geometric structures.

Contribution

It introduces a family of Calabi-Yau manifolds with infinite automorphism groups using Coxeter group theory, and explicitly describes their movable cones and automorphisms.

Findings

The movable cone has a fractal structure related to Kleinian groups.

Explicit examples of automorphisms with positive entropy are provided.

The construction applies to Calabi-Yau manifolds of arbitrary dimension.

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.