Timeline for Isomorphism classes of line bundles with connections
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 2, 2018 at 20:48 | comment | added | Ben McKay | @YosemiteSam: the classic refence is Atiyah, Complex analytic connections in fibre bundles, Transactions of the Amer. Math. Soc. 85 (1957), 181-207. MR 19:172c. | |
| Apr 2, 2018 at 19:55 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 3, 2018 at 18:17 | answer | added | Donu Arapura | timeline score: 1 | |
| Mar 3, 2018 at 17:59 | comment | added | Marion | @YosemiteSam I don't think this statement is quite true. Analytically a connection will define a curvature and that is directly related to the $c_1$, the first Chern class. For a line bundle $c_1$ is far from trivial while indeed $c_2=0$. | |
| Mar 3, 2018 at 17:57 | comment | added | Yosemite Sam | @abx do you have a reference / proof for the fact you mention? (i.e. a vector bundle with connection has trivial chern classes) I'd never heard of it and I'm very interested. | |
| Mar 3, 2018 at 12:56 | history | edited | Marion | CC BY-SA 3.0 |
added 321 characters in body
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| Mar 3, 2018 at 11:45 | comment | added | Marion | What does this notation mean (the $d$ part)? But I do not understand why a vector bundle with connection has trivial Chern classes? Do you mean fixed? | |
| Mar 3, 2018 at 11:39 | comment | added | abx | You are indeed far off. A vector bundle with a connection has trivial Chern classes. For $X=\mathbb{P}^2$, the only line bundle with a connection is $(\mathcal{O}_{\mathbb{P}^2},d)$. | |
| Feb 28, 2018 at 20:44 | history | asked | Marion | CC BY-SA 3.0 |