Picard group and fundamental group of the moduli of Higgs bundles on curves

Abstract

Let $X$ be an irreducible smooth projective curve of genus $g \geq 2$ over $\mathbb{C}$. Let $G$ be a connected reductive affine algebraic group over $\mathbb{C}$. Let $\mathrm{M}_{G, {\rm Higgs}}^δ$ be the moduli space of semistable principal $G$--Higgs bundles on $X$ of topological type $δ\in π_1(G)$. In this article, we compute the fundamental group and Picard group of $\mathrm{M}_{G, {\rm Higgs}}^δ$.