Picard group of moduli of parabolic Higgs bundles

TL;DR

This paper investigates the structure of the Picard groups of moduli spaces of semistable parabolic bundles and Higgs bundles over a compact Riemann surface of genus at least 3, providing insights into their geometric properties.

Contribution

It computes and analyzes the Picard groups of the moduli spaces of semistable parabolic bundles and Higgs bundles, revealing new structural information.

Findings

Determined the Picard group structure of parabolic bundle moduli.

Analyzed the Picard group of parabolic Higgs bundle moduli.

Provided new geometric insights into these moduli spaces.

Abstract

Let $X$ be a compact Riemann surface of genus $g\geq 3$ and let $\mathcal{M}_{\mathrm{par}}$ be the moduli space of semistable parabolic bundles over $X$. Let $\mathcal{M}_{\mathrm{parH}}$ denote the moduli space of semistable parabolic Higgs bundles over $X$. In this article, we study the Picard group of $\mathcal{M}_{\mathrm{par}}$ and $\mathcal{M}_{\mathrm{parH}}$.