Hitchin–Kobayashi Correspondence, Quivers, and Vortices

By Luis Álvarez-Cónsul, O. Garc'ia-Prada. 2001

136 citations recorded by the source corpus.

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 Kähler, 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 Kähler 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.

View Paper: https://www.semanticscholar.org/paper/cc0b57bbfd9770f962c04661e23cd21c44dbcc8e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

The universal Kobayashi-Hitchin correspondence on Hermitian manifolds (2004, background): “tructures (L,(F j) 1≤j≤m). Similarly one can see easily that all classical moduli problems in our list are also special cases of this universal problem, as well as all “quiver problems” considered in [AG]. The main goals of our article are: I. To give the correct stability and polystability conditio”
Homological Algebra of Twisted Quiver Bundles (2002, background): “The length |p| of a non-trivial path p is the number of arrows in the sequence; a trivial path has length zero.”