ScalingStacks

Definition 5.1. [4, Thm. 2.17] (Semipositivity I) Let $\left\lVert\cdot\right\rVert$ be a model metric on $L$, associated to a $\mathbb{Q}$-line bundle $\mathcal{L}$ on a model $\mathcal{X}$ of $X_{K}$. Then

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  the metric $\left\lVert\right\rVert$ is a semipositive model metric iff $\mathcal{L}$ is nef, namely $\mathcal{L}\cdot C\geq 0$ for any projective curve $C$ contained in $\mathcal{X}_{0}$;

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  a continuous metric $\left\lVert\right\rVert e^{-\phi}$ is semipositive iff it is the uniform limit of some sequence of semipositive model metrics on $X_{K}^{an}$.