Moduli spaces of parabolic bundles over $\mathbb{P}^1$ with five marked points

Abstract

This paper considers the moduli spaces/stacks of parabolic bundles (parabolic logarithmic flat bundles and parabolic logarithmic Higgs bundles with given spectrum) of rank 2 and degree 1 over $\mathbb{P}^1$ with five marked points. The foliation and stratification structures on these moduli spaces/stacks are investigated. In particular, we confirm Simpson's conjecture for the moduli space of parabolic logarithmic flat bundles with certain non-special weight system.