Gauge fixing for logarithmic connections over curves and the Riemann-Hilbert-Problem

dc.creatorGantz, Christian
dc.creatorSteer, Brian
dc.date1995-04-29
dc.date.accessioned2026-07-07T09:06:28Z
dc.date.available2026-07-07T09:06:28Z
dc.descriptionWe 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.description29 pages, Latex 2.09
dc.identifierhttps://arxiv.org/abs/alg-geom/9504016
dc.identifierhttp://arxiv.org/abs/alg-geom/9504016
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150016
dc.subjectAlgebraic Geometry
dc.subject14H60 (Primary) 14H30 14F10 14F35 (Secondary)
dc.titleGauge fixing for logarithmic connections over curves and the Riemann-Hilbert-Problem
dc.typetext

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