Definition 17.24.2. Let $X$ be a ringed space and let $f_1, \ldots , f_ n \in \Gamma (X, \mathcal{O}_ X)$. The *Koszul complex on $f_1, \ldots , f_ r$* is the Koszul complex associated to the map $(f_1, \ldots , f_ n) : \mathcal{O}_ X^{\oplus n} \to \mathcal{O}_ X$. Notation $K_\bullet (\mathcal{O}_ X, f_1, \ldots , f_ n)$, or $K_\bullet (\mathcal{O}_ X, f_\bullet )$.

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