Let $X$ be a complex manifold, let $L \to X$ be a holomorphic line bundle, and let $s \in H^0(X,L)$ be a nonzero holomorphic section whose associated effective Cartier divisor $D=(s)_0$ is smooth and reduced. Let $i:D\hookrightarrow X$ denote the inclusion of the resulting closed complex submanifold, and let $\mathcal O_D$ denote its structure sheaf. For every [open set](/page/Open%20Set) $U\subset X$, let $\mathcal O_{D\cap U}:=\mathcal O_D|_{D\cap U}$ denote the restricted structure sheaf, and for every point $x\in D$, let $\mathcal O_{D,x}$ denote the stalk of $\mathcal O_D$ at $x$. Viewing $L$ also as the sheaf of holomorphic sections of $L$, and writing $L|_D$ for the restricted holomorphic line bundle on $D$, there is a short exact sequence of sheaves on $X$:

\begin{align*} 0 \longrightarrow \mathcal O_X \xrightarrow{\cdot s} L \xrightarrow{\operatorname{res}_D} i_*(L|_D) \longrightarrow 0. \end{align*}

Here $\cdot s$ sends a local [holomorphic function](/page/Holomorphic%20Function) $f$ to $fs$, and $\operatorname{res}_D$ is restriction of local sections of $L$ to $D$.