Timeline for Symmetric powers and duals of vector bundles in char p
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 12, 2010 at 5:01 | vote | accept | David Eisenbud | ||
| Sep 12, 2010 at 5:01 | vote | accept | David Eisenbud | ||
| Sep 12, 2010 at 5:01 | |||||
| Aug 5, 2010 at 14:02 | comment | added | Tom Goodwillie | Answering a question that was not asked, I believe it is easy to give examples over $mathbb Z$ of bundles $E$ such that these two symmetric squares of $E$ are nonisomorphic, where the argument does not rely on proving that the bundles are not isomorphic in characteristic $2$. | |
| Aug 4, 2010 at 15:05 | answer | added | Tom Goodwillie | timeline score: 14 | |
| Aug 4, 2010 at 13:21 | answer | added | Torsten Ekedahl | timeline score: 28 | |
| Aug 4, 2010 at 12:34 | comment | added | Torsten Ekedahl | Yes, not only do they have the same Chern classes they give the same element in the Grothendieck group. | |
| Aug 4, 2010 at 11:09 | comment | added | Tom Goodwillie | These two bundles always appear the same in the Grothendieck group, right? | |
| Aug 4, 2010 at 8:37 | comment | added | algori | Torsten -- yes, it is invariant under twisting. My bad. | |
| Aug 4, 2010 at 7:48 | comment | added | Torsten Ekedahl | @algori: It is almost true, up to a twist by a line bundle every vector bundle (on some quasi-projective variety) is the pullback of the tautological bundle on some Grassmannian. The problem is invariant under twisting by line bundles. So yes the problem is equivalent to the same problem for the tautological bundles. | |
| Aug 4, 2010 at 7:18 | comment | added | algori | Angelo -- could you please explain why: as opposed to the topological case, not all algebraic vector bundles are induced from the tautological bundles over Grassmannians. | |
| Aug 4, 2010 at 6:41 | comment | added | Angelo | Hi David! The examples to try would be tautological bundles on grassmannians (if the isomorphim exists for those, then it should always exist, right?). Have you tried with tangent bundles to projective spaces? | |
| Aug 4, 2010 at 0:37 | comment | added | algori | I've added the "Algebraic geometry" tag. | |
| Aug 4, 2010 at 0:36 | history | edited | algori |
added ag tag
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| Aug 3, 2010 at 23:27 | history | asked | David Eisenbud | CC BY-SA 2.5 |