Quiver bundles and wall crossing for chains

• Author(s): Gothen, PB ; Nozad, A
• Date: 2019
• Persistent ID: https://hdl.handle.net/10216/112433
• Origin: Repositório Aberto da Universidade do Porto
• Document Type: Journal article
• Language: English

Description

Holomorphic chains on a Riemann surface arise naturally as fixed points of the natural C-action on the moduli space of Higgs bundles. In this paper we associate a new quiver bundle to the 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 alvarez-Consul-Garcia-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.