Timeline for almost holomorphic line bundles
Current License: CC BY-SA 3.0
3 events
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| Mar 10, 2014 at 14:48 | comment | added | Robert Bryant | Actually, no. The Chern class of $L$ is only a cohomology class in $H^2(M)$; even a choice of $J_L$ does not yield a well-defined $2$-form until one chooses a compatible connection and computes its curvature. Without a more precise definition of what you mean by 'good', I don't think that your question is really answerable. | |
| Mar 9, 2014 at 1:39 | comment | added | Mohammad Farajzadeh-Tehrani | Thanks for sharing your thoughts. I agree with the first paragraph on how the question can be stated. Then in fact, my question is about the existence of a good J_M; generic J_M does not have this property for sure. I am looking for topological or symplectic obstructions against the existence of such J_M. For example, chern class of L is a well-defined 2-form no matter what J is. Then what does the existence of such J impose on this class; if J_M is good, can we conclude that c_1(L) would be (1,1) with respect to J_M? and similar. | |
| Mar 8, 2014 at 22:26 | history | answered | Robert Bryant | CC BY-SA 3.0 |