Example of inclusion which is not a finite morphism - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-06-19T20:50:52Z http://mathoverflow.net/feeds/question/17658 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/17658/example-of-inclusion-which-is-not-a-finite-morphism Example of inclusion which is not a finite morphism Paul Yuryev 2010-03-09T21:41:54Z 2010-03-10T01:00:42Z <p>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?</p> <p>Thanks!</p> <p><strong>Edit:</strong> Sorry this question is very simple, I made a mistake asking the question. For a corrected version, check out <a href="http://mathoverflow.net/questions/17678/example-of-restriction-of-a-finite-morphism-which-is-not-finite" rel="nofollow">this one.</a></p> http://mathoverflow.net/questions/17658/example-of-inclusion-which-is-not-a-finite-morphism/17660#17660 Answer by Qing Liu for Example of inclusion which is not a finite morphism Qing Liu 2010-03-09T21:54:59Z 2010-03-09T21:54:59Z <p>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\$. </p>