Lemma 27.12.2. Let $S$ be a graded ring. Let $X = \text{Proj}(S)$. The open subscheme $U_ d \subset X$ (27.12.0.1) represents the functor $F_ d$ and the triple $(d, \mathcal{O}_{U_ d}(d), \psi ^ d)$ defined above is the universal family (see Schemes, Section 26.15).

**Proof.**
This is a reformulation of Lemma 27.12.1
$\square$

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