Twistor space for local systems on an open curve

Abstract

Let [Formula: see text] be a smooth quasi-projective curve. We previously constructed a Deligne–Hitchin moduli space with Hecke gauge groupoid for connections of rank [Formula: see text]. We extend this construction to the case of any rank [Formula: see text], although still keeping a genericity hypothesis. The formal neighborhood of a preferred section corresponding to a tame harmonic bundle is governed by a mixed twistor structure.