ScalingStacks

Proof. [04XV]

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Proof.

In the proof of Proposition 4.3, we have constructed a dlt pair (๐’ด,๐’ดs)(\mathscr{Y},\mathscr{Y}_{s}) with ๐’ด\mathscr{Y} of finite type over kk such that there exists an isomorphism of kk-schemes ๐’ณkโ†’๐’ดs\mathscr{X}_{k}\to\mathscr{Y}_{s} that identifies the log canonical centers of (๐’ณ,๐’ณk)(\mathscr{X},\mathscr{X}_{k}) contained in ๐’ณk\mathscr{X}_{k} with those of (๐’ด,๐’ดs)(\mathscr{Y},\mathscr{Y}_{s}) contained in ๐’ดs\mathscr{Y}_{s}. Thus the result follows from the corresponding properties of (๐’ด,๐’ดs)(\mathscr{Y},\mathscr{Y}_{s}) proven in [Ko13, 4.16]. โˆŽ

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