Timeline for Chern classes via degeneracy loci
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| S Feb 12, 2021 at 19:49 | history | suggested | Ali Taghavi |
I add two tags.
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| Feb 12, 2021 at 19:13 | review | Suggested edits | |||
| S Feb 12, 2021 at 19:49 | |||||
| Jan 24, 2017 at 20:50 | comment | added | user21574 | the best reference is the lecture note of Laurent Manivel , Symmetric Functions, Schubert Polynomials, and Degeneracy Loci | |
| Sep 2, 2016 at 2:28 | comment | added | user40276 | Maybe I'm being too naive, but doesn't a transversal (to the zero section) section of the form $s_1 \wedge … \wedge s_{r-k + 1}$ would suffice ?Furthermore aren't all section of the exterior product of a smooth vector bundle of this form (exterior product commutes with global sections in the smooth case?)? | |
| Sep 1, 2016 at 8:34 | answer | added | diverietti | timeline score: 4 | |
| Sep 1, 2016 at 1:26 | comment | added | Mohammad Farajzadeh-Tehrani | The case of Euler class is basic. I am definitely talking about the other cases here. I am asking for a reference not believes, otherwise I was told such statement exists. Individually transversal is not enough, the question is what "generic" means in this case for a set of sections. | |
| Aug 31, 2016 at 22:14 | comment | added | user40276 | For the highest chern class (that is the Euler class), you can find a proof in Bott and Tu (pay 135 of maths.ed.ac.uk/~aar/papers/botttu.pdf) that is not detailed at all if not wrong. I believe the general case follows analogously using basic intersection theory as long as you can pick enough transversal sections (I believe this follows from transversality theorem). Of course, you will have to use Poincaré duals instead of irreducible subvarieties. | |
| Aug 31, 2016 at 18:16 | history | asked | Mohammad Farajzadeh-Tehrani | CC BY-SA 3.0 |