ScalingStacks

Theorem 1.1. Let $\phi$ be an asymptotic Fubini-Study metric on $L$. Then for any $\epsilon>0$, there exists $n_{Y}\in\mathbb{N}$ such that, for any $n\geq n_{Y}$ and any $t_{n}\in H^{0}(Y,L|_{Y}^{\otimes n})$, there exits $s_{n}\in V_{n}(L)$ such that $s_{n}|_{Y}=t_{n}$ and

$$\lVert s_{n}\rVert_{n\phi}\leq\mathrm{e}^{n\epsilon}\cdot\lVert t_{n}\rVert_{n\phi|_{Y}}$$