Proposition 5.18.64A902295BB8C

Proposition 5.18.6.4A902295BB8C Let $\pi \colon Y\rightarrow X$ be a proper bimeromorphic morphism from a complex manifold $Y$. Suppose that $\varphi \in \mathrm{QPSH}(X)$ has analytic singularities (resp. has log singularities along an effective $\mathbb {Q}$-divisor $D$). Then $\pi ^*\varphi $ has analytic singularities (resp. has log singularities along $\pi ^*D$).