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Working paper

Stable Bundles on Irregular Vaisman Manifolds

A locally conformally K¨ahler (LCK) manifold is a complex manifold whose universal cover is K¨ahler with monodromy group acting on the universal cover by holomorphic homotheties. A Vaisman manifold M is a compact non-K¨ahler LCK manifold admitting an action of a holomorphic conformal flow lifting to an action on a K¨ahler 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) ≥ 3, is equivariant and filtrable. In the present paper we generalize this result to irregular Vaisman manifolds.