Quasi-parabolic Higgs bundles and null hyperpolygon spaces

Abstract

We introduce the moduli space of quasi-parabolic S L ( 2 , C ) SL(2,\mathbb {C}) -Higgs bundles over a compact Riemann surface Σ \Sigma and consider a natural involution, studying its fixed point locus when Σ \Sigma is C P 1 \mathbb {C} \mathbb {P}^1 and establishing an identification with a moduli space of null polygons in Minkowski 3 3 -space.