Einstein-Hermitian connection on twisted Higgs bundles [Connexions d'Einstein-Hermite sur les fibr?s de Higgs tordus]

摘要

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