Singularities of varieties admitting an endomorphism (by a paper of Broustet and Horing)

We define a volume of an isolated singularity $(X,O)$. For every finite morphism of isolated singularity we relate volumes of singularities. If $X$ is $\mathbb Q$-Gorenstein then $Vol(X,O)=0$ iff $X$ has lc singularities.