Definition 22.1.71EEADED50AAC3

Definition 22.1.71 .EEADED50AAC3 A plurisubharmonic metric (or psh metric for short) on $L^{\mathrm{An}}$ is a function $\phi \colon X^{\mathrm{An}}\rightarrow [-\infty ,\infty )$ that is not identically $-\infty $, and is the pointwise limit of a decreasing net $(\phi _ i)_{i\in I}$, where $\phi _ i\in \mathcal{H}^{\mathrm{gf}}_{\mathbb {Q}}(L_ i^{\mathrm{An}})$ for some $\mathbb {Q}$-line bundles $L_ i$ on $X$ satisfying $c_1(L_ i)\to c_1(L)$ in $\mathrm{NS}^1(X)_{\mathbb {R}}$.