Quasi-parabolic Higgs bundles and null hyperpolygon spaces

Abstract

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

Appendix added. To appear in Trans. Amer. Math. Soc