Timeline for de-Rham moduli space over a compact Riemann surface
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 28, 2021 at 11:53 | comment | added | Nicolast | About the second one: maybe I misunderstood your question: do you want the smoothness of the space of $\Lambda$-connections for all $\lambda$ simultaneously? My answer was only about the smoothness for a fixed $\lambda\neq 0$. | |
| Jan 28, 2021 at 11:48 | comment | added | Nicolast | About your first comment: I confess I never read the proof, but I think you can show the real analyticity of the non abelian Hodge correspondence by simply showing that solutions of Hitchin's equations vary analytically with the parameters. | |
| Jan 28, 2021 at 9:06 | review | Low quality posts | |||
| Jan 28, 2021 at 11:07 | |||||
| Jan 28, 2021 at 8:59 | comment | added | user131608 | Also I dont understand how one can use the Riemann-Hilbert correspondence to argue that the moduli of stable lambda connections is a smooth algebraic variety. At least the arguement given above is not complete and probably your following statement is incorrect "and the moduli space of stable pairs is the Zariski open subset consisting of conjugacy classes of irreducible representations. ". Thank you for your answer. | |
| Jan 28, 2021 at 8:54 | comment | added | user131608 | When we say that there is a real analytic isomorphism between the moduli space of stable Higgs bundles of rank r and degree 0 and the moduli space of rank r λ-connections, we are already using the fact that both these spaces fit into a smooth family. So you have actually assumed what you want to argue. | |
| Jan 27, 2021 at 15:05 | review | First posts | |||
| Jan 27, 2021 at 15:26 | |||||
| Jan 27, 2021 at 14:58 | history | answered | Nicolast | CC BY-SA 4.0 |