Kobayashi—Hitchin correspondence for twisted vector bundles

Abstract

We prove the Kobayashi—Hitchin correspondence and the approximate Kobayashi—Hitchin correspondence for twisted holomorphic vector bundles on compact Kähler manifolds. More precisely, if X is a compact manifold and g is a Gauduchon metric on X, a twisted holomorphic vector bundle on X is g−polystable if and only if it is g−Hermite-Einstein, and if X is a compact Kähler manifold and g is a Kähler metric on X, then a twisted holomorphic vector bundle on X is g−semistable if and only if it is approximate g−Hermite-Einstein.

Keywords

• twisted vector bundles
• semistability
• hermite-einsten metrics
• 32l05
• 53c07
• 14j60
• 53d18
• 53c28
• 53c15
• 15a66
• 32l25