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We study complex Lagrangians in Hitchin systems that factor through a propersubvariety of the Hitchin base non-trivially intersecting the regular locus.This gives a general framework for several examples in the literature. Wecompute the fiber-wise Fourier-Mukai transform of flat line bundles on visibleLagrangians. This proposes a construction of mirror dual branes to visibleLagrangians. Finally, we study a new example of visible Lagrangians in detail.Such visible Lagrangian exists whenever the underlying Riemann surface is apillowcase cover. The proposed mirror dual brane turns out to be closelyrelated to Hausel's toy model.

Visible Lagrangians for Hitchin systems and pillowcase covers