If $K_{X}$ is semi-ample over $C$ and $\mathscr{X}$ is a good minimal $dlt$-model of $X$ over $\mathscr{C}$, then

$$\mathrm{Sk}(X_{K})=\mathrm{Sk}(\mathscr{X}).$$

Moreover, if $m$ is a positive integer such that $mK_{\mathscr{X}}+m(\mathscr{X}_{s})_{\mathrm{red}}$ is Cartier and generated by global sections $\omega_{1},\ldots,\omega_{r}$ over some neighbourhood of $s$ in $\mathscr{C}$, then

(3.3.5)

$$\mathrm{Sk}(X_{K})=\bigcup_{i=1}^{r}\mathrm{Sk}(X_{K},\omega_{i}).$$