Hermitian-Einstein connections on polystable orthogonal and symplectic parabolic Higgs bundles

TL;DR

This paper proves that polystable orthogonal or symplectic parabolic Higgs bundles on a smooth projective curve admit Hermitian-Einstein connections, establishing a correspondence between stability and geometric structure.

Contribution

It extends the Hermitian-Einstein correspondence to orthogonal and symplectic parabolic Higgs bundles on curves, a case not previously covered.

Findings

Polystability is equivalent to the existence of Hermitian-Einstein connections.

The result applies to bundles with parabolic structures over finite subsets.

Establishes a new link between stability conditions and differential geometry for these bundles.

Abstract

Let X be a smooth complex projective curve and S a finite subset of X. We show that an orthogonal or symplectic parabolic Higgs bundle on X with parabolic structure over S admits a Hermitian-Einstein connection if and only if it is polystable.