On holomorphic vector bundles on Hopf manifolds with trivial pullback on the universal covering.
In this paper, we continue the study of the possible cohomology rings of compact complex four dimensional irreducible hyperkähler manifolds. In particular, we prove that in the case b 2=7, b 3=0 or 8. The latter was achieved by the Beauville construction.
We characterize intrinsically two classes of manifolds that can be properly embedded into spaces of the form . The first theorem is a compactification theorem for pseudoconcave manifolds that can be realized as where is a projective variety. The second theorem is an embedding theorem for holomorphically convex manifolds into .
In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold , with 1- dimensional exceptional set and finitely generated second homology group , is embeddable in if and only if is Kähler, and this case occurs only when does not contain any effective curve which is a boundary.
Harvey and Lawson introduced the Kähler rank and computed it in connection to the cone of positive exact currents of bidimension for many classes of compact complex surfaces. In this paper we extend these computations to the only further known class of surfaces not considered by them, that of Kato surfaces. Our main tool is the reduction to the dynamics of associated holomorphic contractions .