We consider geometrically infinite Kleinian groups and, in particular, groups with singly cusped parabolic fixed points. In order to distinguish between different geometric characteristics of such groups, we introduce the notion of horospherical tameness. We give a brief discussion of the fractal nature of their limit sets. Subsequently, we use Jørgensen's analysis of punctured torus groups to give a canonical decomposition into ideal tetrahedra of the geometrically infinite end. This enables us to relate horospherical tameness to Diophantine properties of Thurston's end invariants.

I give a cohomological characterization of semiample line bundles. The result is a generalization of both the Fujita-Zariski Theorem on semiampleness and the Grothendieck-Serre Criterion for ampleness. As an application of the Fujita-Zariski Theorem I characterize contractible curves in 1-dimensional families.

In this paper we introduce a surgery of a certain type on {$K$}-contact manifolds. As an application we classify the diffeomorphism types of all closed simply connected 5-dimensional {$K$}-contact manifolds of rank 3.

Concerning the intergarability of almost Kähler manifolds, it is known the conjecture by S. I. Goldberg that a compact almost Kähler Einstein manifold is Kähler. In this paper, we will give some positive partial answers to the conjecture.

We classify the local and global singularities of sextics which are tame torus curves of type (2,3) and we also show the degenerations among these classes. As an application, two Zariski pairs are found.