Corollary 12.2.4A486E36565B6

Proof. By the definition of bigness, there are a Hermitian form $h$ and $\delta >0$ such that $\theta -\delta h$ is pseudoeffective. Monotonicity, homogeneity and the theorem, applied to $h\in \mathscr P$, give $\lambda _\mu (\theta )\geq \delta \lambda _\mu (h)>0$. $\square$