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 $\mathrm{ M}_{ G, { \rm Higgs}}^{ \delta}$ 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 $\mathrm{ M}_{ G, { \rm Higgs}}^{ \delta}$.
Categories: math.AG