Situation 27.28.1. Let $X$ be a scheme. Let $\mathcal{L}$ be an ample invertible sheaf on $X$. Set $S = \Gamma _*(X, \mathcal{L})$ as a graded ring. Set $Y = \text{Proj}(S)$. Let $f : X \to Y$ be the canonical morphism of Lemma 27.26.9. It comes equipped with a $\mathbf{Z}$-graded $\mathcal{O}_ X$-algebra map $\bigoplus f^*\mathcal{O}_ Y(n) \to \bigoplus \mathcal{L}^{\otimes n}$.

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