Hitchin-Kobayashi correspondence, quivers, and vortices

Details Hitchin-Kobayashi correspondence, quivers, and vortices Hitchin-Kobayashi correspondence, quivers, and vortices

2001-12-16

arxiv.org/abs/math/0112161v2

Commun.Math.Phys. 238 (2003) 1-33

Mathematics

Differential Geometry

28 pages; larger introduction, added references for the introduction, added a short comment in Section 1, typos corrected, acc

Scientific paper

10.1007/s00220-003-0853-1

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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