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projective scheme
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A morphism \(f\) is projective if it factors as a closed immersion into \(\mathbb{P}_{Y}^{n}\), followed by the projection map \(\mathbb{P}_{Y}^{n} \rightarrow Y\) for some \(n\).
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\(f\) is quasiprojective if it factors as an open immersion followed by a projective morphism.
Results
- Every projective variety is complete.
- For a smooth projective variety, the canonical sheaf can be identified with the dualizing sheaf.