Let $X$ be a complex manifold, and let $D$ be a Cartier divisor on $X$. Then $D$ determines a holomorphic line bundle, denoted $\mathcal O(D)$, constructed from any local system of meromorphic defining equations for $D$. If $D$ and $D'$ are Cartier divisors on $X$, then there is a holomorphic line bundle isomorphism \begin{align*} \mathcal O(D + D') \cong \mathcal O(D) \otimes \mathcal O(D'). \end{align*} If $D = (f)$ is the principal divisor of a nonzero global [meromorphic function](/page/Meromorphic%20Function) $f$ on $X$, then $\mathcal O(D)$ is holomorphically isomorphic to the product holomorphic line bundle $X \times \mathbb C$.