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Every closed immersion is a finite morphism. Can you give an example of quasi-projective varieties $X\subset Y$ such that inclusion $X\hookrightarrow Y$ is not finite? Same with Y projective?


Edit: Sorry this question is very simple, I made a mistake asking the question. For a corrected version, check out this one.

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closed as no longer relevant by Harry Gindi, Gjergji Zaimi, Yemon Choi, Scott Morrison Mar 10 '10 at 2:06

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Yes I surely can. Is this homework? What did you try? – Kevin Buzzard Mar 9 '10 at 21:51
Oops... sorry. – Qing Liu Mar 9 '10 at 22:13
You really can't change the question like that. – Harry Gindi Mar 10 '10 at 0:38
Well, at least after you've already received an answer. – Harry Gindi Mar 10 '10 at 0:39
Should I delete and resubmit? – Paul Yuryev Mar 10 '10 at 0:39
up vote 11 down vote accepted

An open immersion is never finite unless it is also a closed immersion (for finite morphisms are proper). So you just need to take a non-empty open subset $X$ which is not a connected component in $Y$.

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