Remark 19.4.23555C64B2D134

Remark 19.4.23.555C64B2D134 It follows from the proof that if $\varphi $ has analytic singularities and $\theta _{\varphi }$ is a Kähler current, then (19.4.21) holds.

If we take a modification $\pi \colon Y\rightarrow X$ such that $\pi ^*\varphi $ has log singularities along an effective $\mathbb {Q}$-divisor $D$ on $Y$, then

This is a very special case of theorem 19.5.26.