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Hitchin-Kobayashi correspondence, quivers, and vortices

Luis Álvarez-Cónsul·Oscar García-Prada
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Abstract

A twisted quiver bundle is a set of holomorphic vector bundles over a complex manifold, labelled by the vertices of a quiver, linked by a set of morphisms twisted by a fixed collection of holomorphic vector bundles, labelled by the arrows. When the manifold is Kaelher, quiver bundles admit natural gauge-theoretic equations, which unify many known equations for bundles with extra structure. In this paper we prove a Hitchin--Kobayashi correspondence for twisted quiver bundles over a compact Kaehler manifold, relating the existence of solutions to the gauge equations to a stability criterion, and consider its application to a number of situations related to Higgs bundles and dimensional reductions of the Hermitian--Einstein equations.

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Luis Álvarez-Cónsul, Oscar García-Prada. 2002-12-16. Hitchin-Kobayashi correspondence, quivers, and vortices. https://doi.org/10.1007/s00220-003-0853-1

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