Definition 27.8.2. Let $S$ be a graded ring. Suppose that $D_{+}(f) \subset \text{Proj}(S)$ is a standard open. A *standard open covering* of $D_{+}(f)$ is a covering $D_{+}(f) = \bigcup _{i = 1}^ n D_{+}(g_ i)$, where $g_1, \ldots , g_ n \in S$ are homogeneous of positive degree.

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