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Example of inclusion which is not a finite morphismEvery closed immersion is a finite morphism. Therefore, restriction of a finite morphism to a closed subset is always a finite morphism itself. Can you give an example of quasi-projective varieties $X\subset Y$, $Z$ and a finite morphism $f:Y\to Z$ such that restriction $f:X\to f(X)$ is not finite? Same with Y -- projective?
PS. Sorry the original version of this question was hilariously stupid.
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Post Reopened by S. Carnahan♦, Anton Geraschenko♦♦
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Every closed immersion is a finite morphism. Therefore, restriction of a finite morphism to a closed subset is always a finite morphism itself. Can you give an example of quasi-projective varieties $X\subset Y$, $Z$ and a finite morphism $f:Y\to Z$ such that restriction $f|_X$ f:X\to f(X)$ is not finite? Same with Y -- projective? PS. Sorry the original version of this question was hilariously stupid. |
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Post Closed as "exact duplicate" by Anton Geraschenko♦♦
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