ScalingStacks

Lemma 3.6 . [03E2]

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Lemma 3.6.

Given a neighborhood N2​(∂𝒱)N_{2}(\partial\mathcal{V}) of ∂𝒱⊂∂Δλ∨≅Σ\partial\mathcal{V}\subset\partial\Delta^{\vee}_{\lambda}\cong\Sigma, there is a δ>0\delta>0 such that

  1. (1)

    If n∈Qvλϵn\in Q^{\lambda^{\epsilon}}_{v}, then ⟨v,𝔛δ​(n)⟩=1\langle v,\mathfrak{X}^{\delta}(n)\rangle=1.

  2. (2)

    If n∈Vw\N2​(∂𝒱)n\in V_{w}\backslash N_{2}(\partial\mathcal{V}), the flow line ℱn\mathcal{F}_{n} through nn is a straight line parallel to ww outside Δλδ∨\Delta^{\vee}_{\lambda^{\delta}}.

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