Definition 16.6.16202451F22A2A

Definition 16.6.16.202451F22A2A Let $\alpha \in \mathrm{H}^{1,1}(X,\mathbb {R})$ be a pseudo-effective class. The volume $\operatorname{vol}\alpha $ of $\alpha $ is defined as

where $T_{\min }$ is a current with minimal singularities in $\alpha $. Note that $\operatorname{vol}\alpha $ is independent of the choice of $T_{\min }$, thanks to theorem 13.13.11.