Timeline for Rationally connected varieties and rational fibrations
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| May 10, 2014 at 16:14 | vote | accept | Puzzled | ||
| Oct 16, 2013 at 23:57 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Oct 16, 2013 at 15:08 | comment | added | Francesco Polizzi | Rational chain connectedness is not a birational property (think of a cone over an elliptic curve, which is rationally 2-connected but whose resolution is only unirational), so my previous argument does not work. At the moment, I do not know. Maybe someone else, more expert on the topic, could answer. | |
| Oct 16, 2013 at 14:51 | comment | added | Puzzled | Thank you very much Francesco. Your argument is clear. Can we say something when the general fiber of $\phi$ is singular and rationally chain connected? For instance can we conclude that $X$ is rationally chain connected? | |
| Oct 16, 2013 at 14:38 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Oct 16, 2013 at 14:36 | comment | added | Francesco Polizzi | Ok, maybe you should have added more background :-) Anyway, the answer to your second question is yes because rational connectedness is a birational property, so just solve the indeterminacy of the rational map $\phi$ and apply Graber-Harris-Starr result. I edited the answer. | |
| Oct 16, 2013 at 14:26 | comment | added | Puzzled | Yes, I knew this theorem. However I was wondering if it is still true when we $f$ is just a rational map and not a morphism and the general fiber of $f$ is just rationally chain connected. | |
| Oct 16, 2013 at 14:07 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Oct 16, 2013 at 14:02 | history | answered | Francesco Polizzi | CC BY-SA 3.0 |