Definition 29.12.1. Let $X$ be a scheme. Let $\{ \mathcal{L}_ i\} _{i \in I}$ be a family of invertible $\mathcal{O}_ X$-modules. We say $\{ \mathcal{L}_ i\} _{i \in I}$ is an *ample family of invertible modules on $X$* if

$X$ is quasi-compact, and

for every $x \in X$ there exists an $i \in I$, an $n \geq 1$, and $s \in \Gamma (X, \mathcal{L}_ i^{\otimes n})$ such that $x \in X_ s$ and $X_ s$ is affine.

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