  We study the summands of the decomposition theorem for the Hitchin system for
$\mathrm{GL}_n$, in arbitrary degree, over the locus of reduced spectral
curves. A key ingredient is a new correspondence between these summands and the
topology of hypertoric quiver varieties. In contrast to the case of meromorphic
Higgs fields, the intersection cohomology groups of moduli spaces of regular
Higgs bundles depend on the degree. We describe this dependence.
