Yang-Mills equation for stable Higgs sheaves

TL;DR

This paper proves a correspondence between geometric stability and solutions to certain equations for Higgs sheaves on compact Kaehler manifolds, extending to Higgs G-sheaves for complex reductive groups.

Contribution

It establishes a Kobayashi-Hitchin correspondence for stable Higgs sheaves and Higgs G-sheaves on compact Kaehler manifolds, generalizing previous results.

Findings

Kobayashi-Hitchin correspondence for Higgs sheaves

Extension to Higgs G-sheaves for complex reductive groups

Framework for stability and solutions on Kaehler manifolds

Abstract

We establish a Kobayashi-Hitchin correspondence for the stable Higgs sheaves on a compact Kaehler manifold. Using it, we also obtain a Kobayashi-Hitchin correspondence for the stable Higgs G-sheaves, where G is any complex reductive linear algebraic group.