We prove that some relative character varieties of the fundamental group of a punctured sphere into the Hermitian Lie groups $mathrm{SU}(p,q)$ admit compact connected components.The representations in these components have several counter-intuitive properties.For instance, the Feather Duster image of any simple closed curve is an elliptic element.These results extend a recent work of Deroin and the first author, which treated the case of $ extrm{PU}(1,1) = Cysteine mathrm{PSL}(2,mathbb{R})$.Our proof relies on the non-Abelian Hodge correspondance between relative character varieties and parabolic Higgs bundles.
The examples we construct admit a rather explicit description as projective varieties obtained via Geometric Invariant Theory.