Let $X$ be a complex manifold, and let $D$ be an effective Cartier divisor on $X$. Let $\mathcal O(D)$ denote the holomorphic line bundle associated to $D$ with the convention that, for local holomorphic defining equations $f_i: U_i \to \mathbb C$ satisfying $D|_{U_i} = \operatorname{div}(f_i)$, its transition functions are