9 – Aut | Fundamental domain

Denote by $\mathbb{D}$ the complete set of
reps. of cong. classes of chambers of $\text{Nef}(X)\cap {\mathcal{P}}_S$ obtained by the Borcherds’ method.

If ${\text{Aut}}_{\mathbf{H}}(D)$ is trivial for all $D\in \mathbb{D}$ then

$$\bigcup _{D\in \mathbb{D}}D$$ is a fundamental domain of the action of $\text{Aut}(X)$ onto $\text{Nef}(X)\cap {\mathcal{P}}_S$.

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