%0 Journal Article
%T Stable Flags and the Riemann-Hilbert Problem
%A Eduardo Corel
%A Elie Compoint
%J Mathematics
%D 2010
%I arXiv
%X We tackle the Riemann-Hilbert problem on the Riemann sphere as stalk-wise logarithmic modifications of the classical R\"ohrl-Deligne vector bundle. We show that the solutions of the Riemann-Hilbert problem are in bijection with some families of local filtrations which are stable under the prescribed monodromy maps. We introduce the notion of Birkhoff-Grothendieck trivialisation, and show that its computation corresponds to geodesic paths in some local affine Bruhat-Tits building. We use this to compute how the type of a bundle changes under stalk modifications, and give several corresponding algorithmic procedures.
%U http://arxiv.org/abs/1003.5021v1