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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?

Thanks!

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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 Yes I surely can. Is this homework? What did you try? – Kevin Buzzard Mar 9 2010 at 21:51
Oops... sorry. – Qing Liu Mar 9 2010 at 22:13
You really can't change the question like that. – Harry Gindi Mar 10 2010 at 0:38
Well, at least after you've already received an answer. – Harry Gindi Mar 10 2010 at 0:39
Should I delete and resubmit? – Paul Yuryev Mar 10 2010 at 0:39
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closed as no longer relevant by Harry Gindi, Gjergji Zaimi, Yemon Choi, Scott Morrison♦ Mar 10 2010 at 2:06

1 Answer

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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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