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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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    $\begingroup$ Yes I surely can. Is this homework? What did you try? $\endgroup$
    – Kevin Buzzard
    Commented Mar 9, 2010 at 21:51
  • $\begingroup$ Oops... sorry. $\endgroup$
    – Qing Liu
    Commented Mar 9, 2010 at 22:13
  • $\begingroup$ You really can't change the question like that. $\endgroup$
    – Harry Gindi
    Commented Mar 10, 2010 at 0:38
  • $\begingroup$ Well, at least after you've already received an answer. $\endgroup$
    – Harry Gindi
    Commented Mar 10, 2010 at 0:39
  • $\begingroup$ Should I delete and resubmit? $\endgroup$
    – Paul Yuryev
    Commented Mar 10, 2010 at 0:39

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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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