ScalingStacks

Theorem 3.2 . [026M]

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Theorem 3.2.

We assume that |.||\raisebox{1.72218pt}{.}| is non-trivial and ℒ\mathscr{L} is an ample invertible sheaf. Fix a closed subscheme YY of XX, l∈H0​(Y,L|Y)l\in H^{0}(Y,\left.{L}\right|_{{Y}}) and a positive number ϵ\epsilon. Then there are a positive integer nn and s∈H0​(X,L⊗n)s\in H^{0}(X,L^{\otimes n}) such that s|Y=l⊗n\left.{s}\right|_{{Y}}=l^{\otimes n} and

‖s‖hn≤en​ϵ​(‖l‖Y,h)n.\|s\|_{h^{n}}\leq e^{n\epsilon}\left(\|l\|_{Y,h}\right)^{n}.

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