Lemma 27.18.5. With hypotheses and notation as in Lemma 27.18.1 above. Assume \mathcal{A}_ d \to \mathcal{B}_ d is surjective for d \gg 0 and that \mathcal{A} is generated by \mathcal{A}_1 over \mathcal{A}_0. Then
U(\psi ) = Y,
r_\psi : Y \to X is a closed immersion, and
the maps \theta : r_\psi ^*\mathcal{O}_ X(n) \to \mathcal{O}_ Y(n) are isomorphisms.
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