Timeline for Morphisms with connected fibres and rational functions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 26, 2016 at 1:56 | comment | added | R. van Dobben de Bruyn | @Mark: you can take $Y'$ to be the integral closure of $Y$ in $L$. If $X$ is normal, then $X \to Y$ has to factor through $Y'$. In this case, a general fibre will be $\mathbb C^d$ (since $Y' \to Y$ is generically finite étale, hence finite étale on some open). Note however that $Y' \to Y$ need not even be flat, so there could be fibres of different length. | |
| Feb 29, 2016 at 15:19 | comment | added | pgraf | See Example 2.1.12 of Lazarsfeld's "Positivity in Algebraic Geometry". | |
| Feb 25, 2016 at 15:49 | comment | added | Jeff Yelton | Yeah, you're right. I suppose the main thing would be to argue that the rational map $Y' \to Y$ is defined on an entire fiber over some closed point of $Y$. | |
| Feb 24, 2016 at 22:32 | comment | added | user47305 | How are you getting the morphism $Y' \to Y$? A map between the function fields gives a dominant rational map, not a morphism. And then some care is needed when talking about the fibers. | |
| Feb 24, 2016 at 13:59 | history | answered | Jeff Yelton | CC BY-SA 3.0 |