. Let $X$ be a compact Kähler manifold and $\chi\in H^{1,1}(X,\mathbb{R})$ a class which is nef and big. Then for all $T\in\chi^{as}_{>0}$ there exists a log resolution $\mu$ of the coherent ideal sheaf ${\cal J}^{kT}$, $\mu^{*}{\cal J}^{kT}={\cal O}(-D)$, an effective divisor $D^{\prime}$ with $|D^{\prime}|=|D|$ and $r\in\mathbb{N}_{>0}$ such that the class $\mu^{*}\chi-2\pi r^{-1}\{D^{\prime}\}$ is Kähler.