Timeline for pushforward of locally free sheaf is locally free?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Sep 29, 2011 at 1:17 | comment | added | J.C. Ottem | I corrected my answer in accordance with your comments. Thanks! | |
| Sep 29, 2011 at 1:14 | history | edited | J.C. Ottem | CC BY-SA 3.0 |
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| Sep 28, 2011 at 18:47 | comment | added | Donu Arapura | Sure, with smooth maps there is no problem. It is also OK for semistable maps, which is why I remembered it that way. | |
| Sep 28, 2011 at 18:39 | comment | added | J.C. Ottem | Yes you are right, I guess I misquoted the theorem. But the OP wanted the morphism to be smooth, so the Du Bois condition with the fibers should be satisfied, right? | |
| Sep 28, 2011 at 18:30 | comment | added | Donu Arapura | JC: I'm sorry if this sounds critical. In fact, I would be happier if it was true unconditionally since I use these sorts of results, but note the sentence: "Si pour tout point geometrique s de la fleche $O_{X_s}\to \Omega_{X_s}^0$ est isomorphisme" Nowadays, we would say the fibres are Du Bois. It is quite a strong condition. | |
| Sep 28, 2011 at 18:24 | comment | added | user2035 | In Theorem 4.6, the condition is on the geometric fibers, not on $X$ itself. | |
| Sep 28, 2011 at 18:03 | comment | added | J.C. Ottem | @Donu: I don't think so? This is Theorem 4.6 in the paper I linked to. | |
| Sep 28, 2011 at 18:01 | comment | added | Will Sawin | Since every vector bundle is locally trivial, one should be able to apply this result locally. | |
| Sep 28, 2011 at 17:54 | comment | added | user2035 | See also mathoverflow.net/questions/23891/… | |
| Sep 28, 2011 at 17:45 | comment | added | user2035 | For $i=0$ only, a similar result is given in EGA III, 7.8.7. | |
| Sep 28, 2011 at 17:41 | comment | added | Donu Arapura | I haven't looked at that paper in a while, but don't need to assume that $f$ is semistable? Should be OK in general when $\dim Y=1$, by semistable reduction. | |
| Sep 28, 2011 at 16:22 | history | edited | J.C. Ottem | CC BY-SA 3.0 |
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| Sep 28, 2011 at 15:59 | history | edited | J.C. Ottem | CC BY-SA 3.0 |
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| Sep 28, 2011 at 15:51 | history | answered | J.C. Ottem | CC BY-SA 3.0 |