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arXiv · 1709.09581

Quiver Bundles and Wall Crossing for Chains

P. B. Gothen·A. Nozad
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Abstract

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 Álvarez-Cónsul, García-Prada and 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.

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P. B. Gothen, A. Nozad. 2018-03-05. Quiver Bundles and Wall Crossing for Chains. https://doi.org/10.1007/s10711-018-0341-6

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