Stable Bundles on Irregular Vaisman Manifolds

Abstract

A locally conformally Kähler (LCK) manifold is a complex manifold whose universal cover is Kähler with monodromy group acting on the universal cover by holomorphic homotheties. A Vaisman manifold $M$ is a compact non-Kähler LCK manifold admitting an action of a holomorphic conformal flow lifting to an action on a Kähler cover by nontrivial homotheties. When the orbits of the action on $M$ are compact, it is known that every stable holomorphic vector bundle over $M$, $\dim (M)\ge 3$, is equivariant and filtrable. In the present paper we generalize this result to irregular Vaisman manifolds.

Paper withdrawn due to an error in the proof of Theorem 4.2.3

References in corpus (1)

• Stable bundles on Hopf manifolds