(1.10) Let $X$ be a smooth and proper $K$-scheme. A model of $X$ is a proper flat $R$-scheme $\mathscr{X}$ endowed with an isomorphism $\mathscr{X}_{K}\to X$. An snc-model of $X$ is a regular model $\mathscr{X}$ such that $\mathscr{X}_{k}$ is a divisor with strict normal crossings. An snc-model is called semistable if $\mathscr{X}_{k}$ is reduced. By the semistable reduction theorem [KKMS73, Ch4§3], there exists a finite extension $K^{\prime}$ of $K$ such that $X\times_{K}K^{\prime}$ has a semistable snc-model over the integral closure of $R$ in $K^{\prime}$.

A dlt-model of $X$ is a normal model $\mathscr{X}$ such that the pair $(\mathscr{X},\mathscr{X}_{k,\mathrm{red}})$ is divisorially log terminal (dlt). We say that a dlt-model is good if every prime component of $\mathscr{X}_{k,\mathrm{red}}$ is $\mathbb{Q}$-Cartier; this is slightly weaker than the usual condition that $\mathscr{X}$ is $\mathbb{Q}$-factorial, but it is sufficient for our purposes. In particular, every snc-model is also a good dlt-model. A dlt-model $\mathscr{X}$ is called minimal if the logarithmic relative canonical divisor $K_{\mathscr{X}/R}+\mathscr{X}_{k,\mathrm{red}}$ is semi-ample. When $X$ is Calabi-Yau, this is equivalent to saying that $K_{\mathscr{X}/R}+\mathscr{X}_{k,\mathrm{red}}$ is torsion; when, moreover, $\mathscr{X}_{k}$ is reduced, then it is equivalent to saying that $K_{\mathscr{X}/R}\sim 0$.