A semi-Kähler, resp. Kähler, resp. smooth Kähler, potential on $V$ is a family $(U_{i},\varphi_{i})_{i\in I}$ where $(U_{i})$ is an open covering of $V$ and $\varphi_{i}$ a psh function, resp. a strongly psh function, resp. a ${\mathcal{C}}^{\infty}$-smooth strongly psh function, on $U_{i}$ such that $\varphi_{i}-\varphi_{j}$ is pluriharmonic on $U_{i}\cap U_{j}$.