Semi-stability for Holomorphic Pairs on Compact Gauduchon Manifolds

Abstract

In this paper, we establish a generalized Hitchin–Kobayashi correspondence between the $\tau $$-semi-stability and the existence of approximate $\tau $$-Hermitian–Einstein structure on holomorphic pair $(E,\phi )$$ over the compact Gauduchon manifold.

Keywords

$\tau $$-semi-stable')">$\tau $$-semi-stable / $\tau $$-Hermitian–Einstein structure')">Approximate $\tau $$-Hermitian–Einstein structure / Holomorphic pair / Gauduchon manifolds