Definition 5.13.14D072C98719AA

Definition 5.13.14.D072C98719AA A plurisubharmonic function on $X$ is a function $\varphi \colon X\rightarrow [-\infty ,\infty )$ such that for any $x\in X$, there exists an open neighborhood $U$ of $x$ in $X$, an integer $n\in \mathbb {N}$, a domain $\Omega \subseteq \mathbb {C}^ n$ and a biholomorphic map $F\colon \Omega \rightarrow U$ such that $F^*(\varphi |_ U)\in \mathrm{PSH}(\Omega )$.

The set of plurisubharmonic functions on $X$ is denoted by $\mathrm{PSH}(X)$.