Problem 24.4.31E16C9C72539

Problem 24.4.3.1E16C9C72539 Let $\alpha $ be a smooth closed real $(1,1)$-form on $X$ whose class is nef with $\int _ X\alpha ^ n>0$, and let $h$ be a Hermitian form on $X$. Prove a positive lower bound for the root volume $\lambda _\mu (\alpha )$ of definition 12.2.1, and rule out the collapse of proposition 24.3.2 along a sequence of Gauduchon metrics minimizing the bigness threshold $\kappa _ h(\alpha )$.