Timeline for Exceptional Curves of a Fibration
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 30, 2018 at 17:51 | comment | added | Jason Starr | Please read "The Original form" of Zariski's Main Theorem, p. 288, Section III.9 of David Mumford, "The Red Book of Varieties and Schemes", Lecture Notes in Math. 1358 (1988), Springer-Verlag, Heidelberg. | |
| Sep 30, 2018 at 12:39 | comment | added | user267839 | @Jason Starr: Do you have this in mind: en.wikipedia.org/wiki/Zariski%27s_connectedness_theorem? If yes, then it just states that fibers under certain conditions for $f$ (e.g.as given in my case) are connected. But the core problem in my "proof" is to show that if $f^{-1}(z) = \{x\}$ is a point then $\mathcal{O}_{Y,z} \cong \mathcal{O}_{X,x}$ must hold. And here the obstacle is to proof that $g_z$ is a finite morphism. I don't see how the connectedness part from ZMT prove this. | |
| Sep 30, 2018 at 10:08 | comment | added | Jason Starr | That follows from Zariski's Main Theorem, namely, the connectedness part. | |
| Sep 30, 2018 at 2:54 | history | edited | user267839 | CC BY-SA 4.0 |
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| Sep 30, 2018 at 2:48 | history | asked | user267839 | CC BY-SA 4.0 |