Timeline for Vector bundle over compact complex manifold which is not holomorphic?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2020 at 13:59 | vote | accept | Nadia SUSY | ||
| Apr 7, 2020 at 10:57 | history | edited | Nadia SUSY | CC BY-SA 4.0 |
added 119 characters in body
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| Apr 7, 2020 at 9:47 | comment | added | Ben McKay | Real line bundles don't admit a complex structure, for example the trivial real line bundle. | |
| Apr 7, 2020 at 9:28 | answer | added | Lev Soukhanov | timeline score: 4 | |
| Apr 7, 2020 at 6:00 | review | Close votes | |||
| Apr 7, 2020 at 19:46 | |||||
| Apr 7, 2020 at 5:41 | comment | added | abx | Complex line bundles on a manifold $X$ are classified by the first Chern class $c_1\in H^2(X,\mathbb{Z})$. If $X$ is a compact Kähler manifold, such a line bundle is holomorphic if and only if $c_1$ is of type $(1,1)$. | |
| Apr 6, 2020 at 21:44 | comment | added | Andy Sanders | Nadia, if you are interested in real vector bundles that don't admit the structure of a complex vector bundle, then you should say so. Because, while not trivial, this can be investigated by methods of algebraic topology. Meanwhile, since you use the word holomorphic in your title, you should specify that you are interested in complex vector bundles, since otherwise it's not clear what you are interested in. I think you might have stumbled into a very deep question on accident. | |
| Apr 6, 2020 at 20:31 | answer | added | freidtchy | timeline score: 3 | |
| Apr 6, 2020 at 12:34 | comment | added | Angelo | The introduction to the paper paper arxiv.org/pdf/1506.08111.pdf contains a good survey of the problem. | |
| Apr 5, 2020 at 12:44 | comment | added | Nadia SUSY | @Thomas: So what are interesting examples of bundles that do not admit almost complex structures? | |
| Apr 4, 2020 at 21:11 | comment | added | user347489 | Related: mathoverflow.net/questions/7304/… | |
| Apr 4, 2020 at 20:49 | history | asked | Nadia SUSY | CC BY-SA 4.0 |