Quasi-projective Schemes, Tag 0B41¶
The Stacks Project Authors. (2026). Quasi-projective Schemes, Tag 0B41.
Cited by¶
1 citation across 1 artifact.
Domain-specific¶
- Quasi-projective variety
- A quasi-projective variety is an algebraic variety that can be realized as a locally closed subset of a projective variety.
Supported in partVerified against the work's full text
The source derives quasi-projectivity of X over S from the existence of a quasi-compact immersion into projective space over S — the relative scheme form of the claim.
“Thus there exists a quasi-compact immersion $i : X \to \mathbf{P}^ n_ S$. Hence $\mathcal{L} = i^*\mathcal{O}_{\mathbf{P}^ n_ S}(1)$ is $f$-very ample. As $X \to S$ is quasi-compact we conclude from Morphisms, Lemma 29.39.2 that $\mathcal{L}$ is $f$-ample. Thus $X \to S$ is quasi-projective by definition.”
- A quasi-projective variety is an algebraic variety that can be realized as a locally closed subset of a projective variety.
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