ScalingStacks

Definition 3.11 . [00A2]

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Definition 3.11.

(cf. section 3.4) We say ‖⋅‖C​Y\left\lVert\cdot\right\rVert_{CY} satisfies the NA MA-real MA comparison property, if there exists a semistable snc model (𝒳,ℒ)(\mathcal{X},\mathcal{L}) of (X,L)(X,L) with the property that, the potential ϕ0\phi_{0} defined by ‖⋅‖C​Y=‖⋅‖ℒ​e−ϕ0\left\lVert\cdot\right\rVert_{CY}=\left\lVert\cdot\right\rVert_{\mathcal{L}}e^{-\phi_{0}} satisfies ϕ0=ϕ0∘r𝒳\phi_{0}=\phi_{0}\circ r_{\mathcal{X}} on the preimages of the retraction map over all the nn-dimensional open faces Int​(ΔJ)⊂S​k​(X)\text{Int}(\Delta_{J})\subset Sk(X).

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