Timeline for Transition matrix for holomorphic vector bundles [closed]
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2011 at 8:01 | history | closed |
David Roberts♦ Deane Yang Torsten Ekedahl Ryan Budney Dan Petersen |
too localized | |
| Sep 19, 2011 at 0:41 | answer | added | september | timeline score: 0 | |
| Sep 19, 2011 at 0:26 | comment | added | september | @Deane: Thank for your answer. I tried to find some natural local triviality for the vector bundles in the examples, but was not successful. After posting this question and seeing your answer, I thought a little more and found the local trivialities. | |
| Sep 18, 2011 at 6:27 | answer | added | Sasha | timeline score: 1 | |
| Sep 18, 2011 at 1:06 | comment | added | Deane Yang | I view this question as a good exercise for someone learning the subject. Many of us had to sort this out when we were students, and it was a useful experience in sorting out the definitions. The point is that with your definitions, you can write down a basis of sections on appropriately chosen open sets and then you can figure out how two different bases are related on the intersection of two such open sets. | |
| Sep 18, 2011 at 0:14 | history | edited | september | CC BY-SA 3.0 |
added 285 characters in body
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| Sep 18, 2011 at 0:05 | comment | added | september | @David: Thanks for fixing Latex. For the open cover we can choose for example the usual cover by the sets $U_i=\{z_i\not= 0\}$. You are right, so my question should be this: How can we write a local trivial for the vector bundle in Question 2? The same for Example 1, assuming that we start from zero, not knowing that $J$ is isomorphic to $[-H]$. | |
| Sep 17, 2011 at 23:57 | comment | added | David Roberts♦ | I fixed the latex. What do you mean by 'the transition matrix' for example 2? The transition functions depend on the choice of open cover. They also depend on a choice of local trivialisation. There is in general no abstract technique. 'Some description' is not a very helpful starting point. | |
| Sep 17, 2011 at 23:51 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
Fixed latex
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| Sep 17, 2011 at 23:37 | history | asked | september | CC BY-SA 3.0 |