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

Abstract

Let $X$ be an irreducible smooth projective curve of genus $g\ge 2$ over $\mathbb{C}$. Let $G$ be a connected reductive affine algebraic group over $\mathbb{C}$. Let ${\mathrm{M}}_{G,\mathrm{Higgs}}^{\delta }$ be the moduli space of semistable principal $G$--Higgs bundles on $X$ of topological type $\delta \in {\pi }_1(G)$. In this article, we compute the fundamental group and Picard group of ${\mathrm{M}}_{G,\mathrm{Higgs}}^{\delta }$.

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