Hermitian-Einstein connections on polystable parabolic principal Higgs bundles

TL;DR

This paper proves the existence of Hermitian-Einstein connections on polystable parabolic principal Higgs bundles over complex projective varieties with divisors, extending the theory to include parabolic structures and Higgs fields.

Contribution

It establishes the existence of Hermitian-Einstein connections for a new class of parabolic principal Higgs bundles with specific boundary conditions.

Findings

Existence of Hermitian-Einstein connections proven

Applicable to polystable parabolic principal Higgs bundles

Extends previous results to include Higgs fields and parabolic structures

Abstract

Given a smooth complex projective variety X and a smooth divisor D on X, we prove the existence of Hermitian-Einstein connections, with respect to a Poincar\'e-type metric on X - D, on polystable parabolic principal Higgs bundles with parabolic structure over D, satisfying certain conditions on its restriction to D.