Einstein-Hermitian connection on twisted Higgs bundles (Pre-published Version)

Abstract

Let X be a smooth projective variety over C. We prove that a twisted Higgs vector bundle (E , θ) on X admits an Einstein–Hermitian connection if and only if (E , θ) is polystable. A similar result for twisted vector bundles (no Higgs fields) was proved in [10]. Our approach is simpler.