Approximate Hermitian-Yang-Mills structures on semistable principal Higgs bundles

TL;DR

This paper extends the Hitchin-Kobayashi correspondence to principal Higgs bundles, establishing that semistability is equivalent to the existence of approximate Hermitian-Yang-Mills structures on such bundles over compact Kähler manifolds.

Contribution

It generalizes the correspondence to principal Higgs bundles with reductive structure groups, linking semistability to approximate Hermitian-Yang-Mills structures.

Findings

Semistability implies existence of approximate Hermitian-Yang-Mills structures.

The correspondence holds for principal Higgs bundles on compact Kähler manifolds.

Provides a characterization of semistability in terms of geometric structures.

Abstract

We generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.