Gauge fixing for logarithmic connections over curves and the Riemann-Hilbert-Problem
| dc.creator | Gantz, Christian | |
| dc.creator | Steer, Brian | |
| dc.date | 1995-04-29 | |
| dc.date.accessioned | 2026-07-07T09:06:28Z | |
| dc.date.available | 2026-07-07T09:06:28Z | |
| dc.description | We explain in detail the correspondence between algebraic connections over CP^{1}, logarithmic at X = { x_{1},...,x_{n} } \subset CP^{1}, and flat bundles over CP^{1}-X with integer weighted filtrations near each x_{j}. Included is a gauge fixing theorem for logarithmic connections. (Thus far, one could work over any Riemann surface.) We prove a bound on the splitting type of a semi-stable logarithmic connection over CP^{1}. Using this we extend and simplify some results on the Riemann-Hilbert-Problem, which asks for a logarithmic connection on a holomorphically trivial bundle over CP^{1}, extending a given flat bundle over CP^{1}-X. The work is self contained and elementary, using only basic knowledge of Gauge Theory and the Birkhoff-Grothendieck-Theorem. | |
| dc.description | 29 pages, Latex 2.09 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9504016 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9504016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150016 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H60 (Primary) 14H30 14F10 14F35 (Secondary) | |
| dc.title | Gauge fixing for logarithmic connections over curves and the Riemann-Hilbert-Problem | |
| dc.type | text |