ScalingStacks

Lemma 4.2 . [04XQ]

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Lemma 4.2.

Let ๐’ณ\mathscr{X} be a normal RR-scheme and let DD be a reduced effective divisor on ๐’ณ\mathscr{X} such that DD contains the singular locus of ๐’ณ\mathscr{X} and such that the pair (๐’ณ,D)(\mathscr{X},D) is dlt. Assume that K๐’ณ/R+DK_{\mathscr{X}/R}+D is Cartier. Then ๐’ณ\mathscr{X} is terminal; in particular, it is regular in codimension two.

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