Abstract The paper is part of an attempt understanding non-Kähler threefolds. We start by looking at compact complex threefolds with algebraic dimension two and admitting lcK metrics. Under certain assumptions, we prove that they are blown-up quasi-bundles over a projective surface.

We introduce and discuss a definition of approximation of a topological algebraic system A by finite algebraic systems of some class K. For the case of a discrete algebraic system this definition is equivalent to the well-known definition of a local embedding of an algebraic system A in a class K of algebraic systems. According to this definition A is locally embedded in K iff it is a subsystem...

Our purpose in this paper is to continue the algebraic study of complex local systems on complex algebraic varieties. We prove a RiemannRoch theorem for these objects using algebraic Chern-Simons characteristic classes. A complex local system E on a smooth, projective complex variety X gives rise to a locally free analytic sheaf E := E ⊗C O an X which (using GAGA) admits a canonical algebraic s...