LAUSR

Holomorphic chains on a Riemann surface arise naturally as fixed points of the natural $$\mathbb {C}^*$$C∗-action on the moduli space of Higgs bundles. In this paper we associate a new quiver bundle to the $${{\mathrm{Hom}}}$$Hom-complex of two chains, and prove that stability of the chains implies stability of this new quiver bundle. Our approach uses the Hitchin–Kobayashi correspondence for quiver bundles. Moreover, we use our result to give a new proof of a key lemma on chains (due to Álvarez-Cónsul–García-Prada–Schmitt), which has been important in the study of Higgs bundle moduli; this proof relies on stability and thus avoids the direct use of the chain vortex equations.