Timeline for moduli space of flat connections $SU(N)$ on an elliptic curve is $\mathbb{C}P^{N-1}$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| May 1, 2017 at 17:05 | vote | accept | john mangual | ||
| Apr 26, 2017 at 16:46 | comment | added | Sebastian | A flat unitary line bundle is just a line bundle equipped with a flat unitary connection $\nabla$. Its $(0,1)$-part $\bar\partial=\tfrac{1}{2}(\nabla+i*\nabla)$ is gives a so called holomorphic structure, as locally there is always a non-vanishing section in the kernel of $\bar\partial$ and two sections in the kernel differ (multiplicatively) by a holomorphic function. This makes the flat unitary line bundle into a holomorphic line bundle, and this correspondence is 1 to 1. This does not only work for line bundles, and is also known as the Narasimhan-Seshadri correspondence. | |
| Apr 26, 2017 at 14:22 | comment | added | john mangual | can you clarify that last part? what is a "flat unitary line bundle" and the "underlying" holomorphic structure. maybe I need to work this out for a specific elliptic curve $E$ | |
| Apr 26, 2017 at 7:52 | history | edited | Ben McKay | CC BY-SA 3.0 |
spelling, grammar
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| Apr 26, 2017 at 7:34 | history | answered | Sebastian | CC BY-SA 3.0 |