Timeline for Inverse problem of Chern Classes
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jul 22, 2020 at 8:17 | answer | added | user161534 | timeline score: 0 | |
| May 19, 2015 at 21:02 | vote | accept | Temitope.A | ||
| May 5, 2015 at 4:44 | answer | added | Qiaochu Yuan | timeline score: 8 | |
| May 4, 2015 at 19:59 | comment | added | Gunnar Þór Magnússon | For your edit, if you're doing complex geometry you could look at Clare Voisin's articles showing that the naive generalization of the Hodge conjecture to Kahler manifolds is false, that is, that the Chern classes of vector bundles or coherent sheaves are not enough to generate the rational classes: webusers.imj-prg.fr/~claire.voisin/Articlesweb/hodgeimrn.pdf | |
| May 4, 2015 at 17:24 | history | edited | Temitope.A | CC BY-SA 3.0 |
added 302 characters in body
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| May 4, 2015 at 16:40 | answer | added | Liviu Nicolaescu | timeline score: 17 | |
| May 4, 2015 at 15:58 | comment | added | Temitope.A | No, I do not restrict the rank of the bundle. In fact, what sparkled this was Bott Residue formula, which holds when the form being integrated is a symmetric polynomial of (formal roots of) chern classes. So I asked my self, how many forms can we see as chern classes of a certain bundle so that I can apply the formula more often? Of course an higher dimensional bundle could make the other side of the formula more difficult. Your comment is interesting, I will think about it! | |
| May 4, 2015 at 15:49 | answer | added | user69091 | timeline score: 6 | |
| May 4, 2015 at 15:42 | comment | added | Jason Starr | Do you restrict the rank of the bundle (for fixed degree of the Chern class)? If so, I think the problem is difficult. Here is another issue: the Chern classes do not uniquely determine a complex vector bundle up to equivalence. To see this, consider the case when the base manifold is an odd-dimensional sphere, so that the Chern classes are all zero. Since homotopy groups with odd degree of the classifying space can be nontrivial, the Chern classes are not sufficient to characterize complex vector bundles. | |
| May 4, 2015 at 15:32 | history | edited | Yemon Choi | CC BY-SA 3.0 |
added top-level tag; minor spelling corrections
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| May 4, 2015 at 15:27 | review | First posts | |||
| May 4, 2015 at 15:47 | |||||
| May 4, 2015 at 15:25 | history | asked | Temitope.A | CC BY-SA 3.0 |