The Hitchin--Kobayashi Correspondence for Quiver Bundles over Generalized Kähler Manifolds

Abstract

In this paper, we establish the Hitchin--Kobayashi correspondence for the $I_{\pm }$-holomorphic quiver bundle $\mathcal{E}=(E,\varphi )$ over a compact generalized Kähler manifold $(X,I_{+},I_{-},g,b)$ such that $g$ is Gauduchon with respect to both $I_{+}$ and $I_{-}$, namely $\mathcal{E}$ is $(\alpha ,\sigma ,\tau )$-polystable if and only if $\mathcal{E}$ admits an $(\alpha ,\sigma ,\tau )$-Hermitian--Einstein metric.

To appear in The Journal of Geometric Analysis