Proposition 3.1. Assume \(X\) is proper. Then, if for all \(\mathscr{F}\) is coherent on \(X\), \begin{align*} h^{1}\left({\mathcal{F}}\otimes {\mathcal{L}}^{\otimes n}\right)=0 \end{align*} for \(i>0\) if \(n \gg 0\).
Proposition 3.1. Assume \(X\) is proper. Then, if for all \(\mathscr{F}\) is coherent on \(X\), \begin{align*} h^{1}\left({\mathcal{F}}\otimes {\mathcal{L}}^{\otimes n}\right)=0 \end{align*} for \(i>0\) if \(n \gg 0\).