Timeline for Line bundles: from transition functions to divisors
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
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| Feb 27, 2010 at 15:06 | answer | added | Pavel Etingof | timeline score: 4 | |
| Feb 27, 2010 at 14:40 | comment | added | t3suji | As you mention, local systems are bundles equipped with flat connections. This means that, first of all, you only get line bundles of degree $d=0$, and secondly, it is not true that the assignment of a line bundle to $\lambda,\mu$ is one-to-one (because you forget the connection). For a curve of any genus, the variety of rank one local systems is isomorphic to $({\mathbb C}^\times)^{2g}$, and the variety of degree zero line bundles is a complex torus $J$ (its Jacobian). $J$ is identified with a quotient of $({\mathbb C}^\times){2g}$ by a subgroup isomorphic to ${\mathbb C}^g$. | |
| Feb 27, 2010 at 11:32 | history | asked | Saul Glasman | CC BY-SA 2.5 |