Let $X$ be a complex manifold, and let $Y \subset X$ be a smooth effective divisor. Let $N_{Y/X} := T_X|_Y / T_Y$ denote the holomorphic normal bundle of $Y$ in $X$. With the convention that $\mathcal{O}_X(Y)$ is the holomorphic line bundle associated to $Y$ and has its canonical section $s_Y$ vanishing precisely along $Y$, there is a canonical holomorphic line bundle isomorphism

\begin{align*} N_{Y/X} \cong \mathcal{O}_X(Y)|_Y. \end{align*}