A weight two phenomenon for the moduli of rank one local systems on open varieties

2007/10/15 by Simpson, Carlos T.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0710.2800

Abstract

The twistor space of representations on an open variety maps to a weight two space of local monodromy transformations around a divisor component at infinty. The space of σ-invariant sections of this slope-two bundle over the twistor line is a real 3 dimensional space whose parameters correspond to the complex residue of the Higgs field, and the real parabolic weight of a harmonic bundle.

Related

• Twistor space for local systems on an open curve
• Twistor Hecke eigensheaves in genus 2
• Involutions of rank 2 Higgs bundle moduli spaces
• A characterization of semisimple local system by tame pure imaginary pluri-harmonic metric
• Hilbert schemes as moduli of Higgs bundles and local systems