Timeline for Extension of a holomorphic vector bundle
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 7, 2010 at 15:19 | vote | accept | Fei YE | ||
| Jan 6, 2010 at 16:16 | comment | added | Fei YE | Thanks! I think however, in general, it is very hard to find a holomorphic connection on a vector bundle over projective space. It is well-known that if a holomorphic connection exists, then the vector bundle splits into line bundles. As for the first question, is there any criterion on that the extension is a vector bundle? I mean necessary and sufficient conditions. Any reference on this subject? | |
| Jan 6, 2010 at 15:02 | comment | added | t3suji | If the connection is not holomorphic, the question is not particularly interesting, but here it goes: Take $E$ to be trivial rank one bundle. It extends to trivial rank one bundle. A connection on such an object is a differential form. Let coefficients of this differential form be smooth functions with a singularity at $(1:0:\dots:0)$. | |
| Jan 6, 2010 at 6:08 | comment | added | Fei YE | If the connection is not holomorphic, how to give a counter example? | |
| Jan 6, 2010 at 5:21 | history | answered | t3suji | CC BY-SA 2.5 |