Hermitian-Einstein Metrics on Parabolic Bundles over compact complex surfaces

TL;DR

This paper establishes a correspondence between Hermitian-Einstein metrics and stable parabolic bundles on certain non-Kähler complex surfaces and manifolds, extending classical results to broader geometric contexts.

Contribution

It proves the Kobayashi-Hitchin correspondence for parabolic bundles over non-Kähler surfaces and higher-dimensional manifolds with specific divisors, broadening the scope of existing theories.

Findings

Proves the Kobayashi-Hitchin correspondence in new geometric settings.

Extends the theory to non-Kähler complex surfaces and higher-dimensional manifolds.

Handles cases with simple normal crossing divisors and smooth divisors.

Abstract

We prove the Kobayashi-Hitchin correspondence for parabolic bundles over compact nonK\"{a}hler surfaces with simple normal crossing divisor or compact nonK\"{a}hler manifolds of any dimension with smooth divisor.