Polystable bundles and representations of their automorphisms

Abstract

Using a quasi-linear version of Hodge theory, holomorphic vector bundles in a neighbourhood of a given polystable bundle on a compact Kähler manifold are shown to be (poly)stable if and only if their corresponding classes are (poly)stable in the sense of geometric invariant theory with respect to the linear action of the automorphism group of the bundle on its space of in˝nitesimal deformations.

Keywords

• kähler
• polystable
• hermite-einstein
• geometric invariant theory
• 53c07
• 14l24
• 32g13
• 32l10
• 32q15