Stable Flags and the Riemann-Hilbert Problem

Autor:	Corel, Eduardo, Compoint, Elie
Rok vydání:	2010
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Algebraic Geometry
Zdroj:	Pacific J. Math. 263 (2013) 283-352
Druh dokumentu:	Working Paper
DOI:	10.2140/pjm.2013.263.283
Popis:	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. Comment: 39 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1003.5021 Zobrazit plný text záznamu View this record from Arxiv