1998/08/01 by Hélène Esnault, Esnault, Hélène, Eckart Viehweg +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Bundle #Differential (mechanical device) #FOS: Mathematics #Genus #Group (periodic table) #Irreducible representation #Line bundle #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Representation (politics) #Vector bundle #math.AG
paper · pdf · doi:10.48550/arxiv.math/9808001
Latex 2e, 10 pages
arxiv created 1998/08/01 · openalex publication_date 1998/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This note is an attempt to generalize Bolibruch's theorem from the projective line to curves of higher genus. We show that an irreducible representation of the fundamental group of an open in a curve of higher genus has always a representation as a regular system of differential equations on a semistable bundle of degree 0. Vice-versa, we show that given such a bundle and 3 points on the curve, one can construct an irreducible representation of the curve minus the 3 points such that an associated regular system of differential equations lives on this bundle.