Let $X$ be a complex manifold, let $M \to X$ be a holomorphic line bundle, and let $x \in X$. Let $\mathcal O_X$ denote the sheaf of holomorphic functions on $X$, let $\mathcal I_x \subset \mathcal O_X$ be the ideal sheaf of germs vanishing at $x$, let $M$ also denote the sheaf of holomorphic sections of the line bundle, and let $M|_x$ denote the fibre of the line bundle at $x$. If

\begin{align*} H^1(X,M \otimes_{\mathcal O_X} \mathcal I_x)=0, \end{align*}

then the evaluation map $\operatorname{ev}_x:H^0(X,M) \to M|_x$, defined by $\operatorname{ev}_x(s)=s(x)$, is surjective. If the above vanishing holds for every $x \in X$, then $M$ is globally generated, meaning that $\operatorname{ev}_y:H^0(X,M) \to M|_y$ is surjective for every $y \in X$.