# Quasi-parabolic Higgs bundles and null hyperpolygon spaces

## TL;DR

This paper introduces a new moduli space of quasi-parabolic Higgs bundles on Riemann surfaces and links its fixed points to null polygons in Minkowski space, revealing geometric structures in complex algebraic geometry.

## Contribution

It defines the moduli space of quasi-parabolic Higgs bundles and establishes a novel correspondence with null hyperpolygon spaces in Minkowski 3-space.

## Key findings

- Identification of fixed point loci with null polygon moduli spaces
- Establishment of a geometric link between Higgs bundles and Minkowski space polygons
- New insights into the structure of Higgs bundle moduli 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.