Timeline for Bertini theorems for base-point-free linear systems in positive characteristics
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 8, 2011 at 16:03 | answer | added | Karl Schwede | timeline score: 3 | |
| Aug 23, 2011 at 16:32 | answer | added | Anton Geraschenko | timeline score: 5 | |
| Jun 10, 2011 at 14:47 | comment | added | Karl Schwede | I sort of hope for some separability/tameness assumptions might be enough. Generically unramified would be great, but think that's not sufficient. | |
| Jun 10, 2011 at 11:43 | comment | added | Thomas Nevins | Hi Karl, I remember thinking about this at the time I wrote the paper and I think you can weaken it (though I don't remember what's proven in Jouanolou). Sorry I can't be more precise. Given the Frobenius pull-back counterexample, though, what kind of alternative would you want to an unramified-ness assumption? | |
| Jun 10, 2011 at 2:49 | comment | added | Karl Schwede | Tom, thanks. I still have to procure my copy of Jounalou, but your paper at least states it if the morphism is unramified, and refers to Theorem 6.3 in that book. To me, unramified is a very strong condition. But perhaps one can weaken it somewhat (in some generic way as you suggest). | |
| Jun 9, 2011 at 21:39 | comment | added | Thomas Nevins | Karl, Ulrich is right that Jouanolou has a strong version (I'm travelling but there should be a precise reference in my "Mirabolic Langlands/quantum Calogero-Moser" paper, though perhaps that's not the precise result from Jouanolou you need). I think it's along the lines of generically unramified maybe? | |
| Jun 9, 2011 at 12:30 | history | edited | Karl Schwede | CC BY-SA 3.0 |
Fixed typo
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| Jun 9, 2011 at 8:16 | comment | added | naf | Have you looked at Jouanolou's "Theoremes de Bertini et Applications"? I haven't looked at it recently, so don't remember the details, but I think that what he proves is close to the best possible. | |
| Jun 9, 2011 at 0:06 | history | asked | Karl Schwede | CC BY-SA 3.0 |