Timeline for Birational morphisms from smooth variety to normal are iso in codim 2
Current License: CC BY-SA 3.0
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| Sep 9, 2017 at 12:43 | comment | added | Sándor Kovács | Or you can use Zariski's Main Theorem. That implies that if $\pi$ is not an isomorphism over $y\in Y$, then $\dim \pi^{-1}(y)>0$, so the locus where it is not an isomorphism can have dimension at most $\dim Y-2$. | |
| Sep 9, 2017 at 7:38 | comment | added | abx | Yes. Since $\operatorname{Sing}(Y) $ has codimension $\geq 2$, you can take it out and assume that $Y$ is smooth. Then you can apply Van der Waerden purity theorem (EGA IV.21.12.12); the proof is much easier in your case but I have no time to look for a referene. | |
| Sep 9, 2017 at 3:57 | history | asked | Din | CC BY-SA 3.0 |