ScalingStacks

Corollary 1.2 . [0258]

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Corollary 1.2.

Assume that the invertible sheaf LL is ample, then the following conditions are equivalent.

  1. (a)

    λh​(l)=0\lambda_{h}(l)=0,

  2. (b)

    for any ϵ>0\epsilon>0, there exists n∈ℕ≥1n\in\mathbb{N}_{\geq 1} and a section s∈H0​(X,L⊗n)s\in H^{0}(X,L^{\otimes n}) such that s|Y=ln{\left.{s}\right|_{{Y}}}=l^{n} and that ‖s‖h≤eϵ​n​‖l‖Y,h\|s\|_{h}\leq e^{\epsilon n}\|l\|_{Y,h}.

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