Hermitian–Einstein connections on polystable parabolic principal Higgs bundles

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 Poincaré-type metric on $X \setminus D$, on polystable parabolic principal Higgs bundles with parabolic structure over $D$, satisfying certain conditions on their restriction to $D$.