ScalingStacks

Lemma 4.9 . [00AJ]

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Lemma 4.9.

Given 0<δ≪10<\delta\ll 1, then for 0<ϵ≪10<\epsilon\ll 1 depending on δ\delta, and tt small enough depending on ϵ,δ\epsilon,\delta,

∫Log𝒳−1​(Wδ)d⁡(ψt−ϕC​Y,t)∧dc​(ψt−ϕC​Y,t)∧(d​dc​ϕ0∘Log𝒳)n−1≤C​δ|log⁡|t||n,\int_{\text{Log}_{\mathcal{X}}^{-1}(W_{\delta})}d(\psi_{t}-\phi_{CY,t})\wedge d^{c}(\psi_{t}-\phi_{CY,t})\wedge(dd^{c}\phi_{0}\circ\text{Log}_{\mathcal{X}})^{n-1}\leq\frac{C\delta}{|\log|t||^{n}},

where CC is independent of δ,ϵ,t\delta,\epsilon,t.

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