Definition 16.8.24E959BD934C4

Definition 16.8.2.4E959BD934C4 For $\varphi ,\psi \in \mathrm{QPSH}(X)$, we say $\varphi $ is $P$-more singular than $\psi $ and write $\varphi \preceq _ P \psi $ if for some (equivalently, every, due to 16.8.4 below) closed smooth real $(1,1)$-form $\theta $ on $X$ such that $\varphi ,\psi \in \mathrm{PSH}(X,\theta )_{>0}$, we have

If $\varphi \preceq _ P \psi $ and $\psi \preceq _ P \varphi $, we write $\varphi \sim _ P \psi $ and say that $\varphi $ and $\psi $ have the same $P$-singularity type.