Semistable bundles on curves and irreducible representations of the fundamental group
Abstract
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. Viceversa, 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 1998
 DOI:
 10.48550/arXiv.math/9808001
 arXiv:
 arXiv:math/9808001
 Bibcode:
 1998math......8001E
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 Latex 2e, 10 pages