Hermitian-Einstein metrics on stable vector bundles over compact K\"ahler orbifolds

TL;DR

This paper establishes the equivalence between slope stability and the existence of Hermitian-Einstein metrics on holomorphic vector bundles over compact K"ahler orbifolds, extending classical results to orbifold settings.

Contribution

It generalizes the Donaldson-Uhlenbeck-Yau theorem to the context of compact K"ahler orbifolds, linking stability to Hermitian-Einstein metrics.

Findings

Slope stability is equivalent to the existence of Hermitian-Einstein metrics.

Properness of a Donaldson-type functional characterizes stability.

Extension of classical theorems to orbifold settings.

Abstract

For a holomorphic vector bundle over a compact K\"ahler orbifold, the slope stability of the bundle is shown to be equivalent to the existence of a Hermitian-Einstein metric or to the properness of a certain functional introduced by Donaldson.