Timeline for A holomorphic vector bundle structure for $\Omega^{(0,1)}(M)$
Current License: CC BY-SA 3.0
8 events
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| May 6, 2015 at 13:47 | comment | added | Falertu Jopanos | So David Speyer's answer is exactly what I'm looking for. How does one go about accepting an answer from another question? Sorry, I'm new here. | |
| May 5, 2015 at 16:02 | comment | added | Matthias Wendt | Well, David Speyer's answer linked above seems to claim that $\Omega^{(0,1)}$ can always be given a holomorphic structure. This should not be unique; when $M$ is an elliptic curve, $\Omega^{(0,1)}$ is trivial, but there are many non-trivial holomorphic line bundles whose underlying complex line bundle is trivial. | |
| May 5, 2015 at 15:50 | history | edited | Falertu Jopanos | CC BY-SA 3.0 |
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| May 5, 2015 at 15:41 | comment | added | Falertu Jopanos | So what about: "When can $\Omega^{(0,1)}$ be given a holomorphic structure"? | |
| May 5, 2015 at 15:38 | comment | added | Matthias Wendt | a slight variation: if $\Omega^{(0,1)}(M)$ happens to be trivial as a complex vector bundle, then obviously it is possible to put the trivial holomorphic structure on it. This happens e.g. for an elliptic curve. Maybe I got something wrong, but the "can never be given a holomorphic structure" seems to weak to be true. | |
| May 5, 2015 at 15:36 | comment | added | Matthias Wendt | You might want to have a look at David Speyer's answer to MO-question mathoverflow.net/questions/8484 | |
| May 5, 2015 at 14:43 | review | First posts | |||
| May 5, 2015 at 15:08 | |||||
| May 5, 2015 at 14:34 | history | asked | Falertu Jopanos | CC BY-SA 3.0 |