  Using a quasi-linear version of Hodge theory, holomorphic vector bundles in a
neighbourhood of a given polystable bundle on a compact Kaehler 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
infinitesimal deformations.
