Definition 31.14.8. Let $X$ be a scheme. Let $\mathcal{L}$ be an invertible sheaf. Let $s \in \Gamma (X, \mathcal{L})$ be a global section. The zero scheme of $s$ is the closed subscheme $Z(s) \subset X$ defined by the quasi-coherent sheaf of ideals $\mathcal{I} \subset \mathcal{O}_ X$ which is the image of the map $s : \mathcal{L}^{\otimes -1} \to \mathcal{O}_ X$.

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