The best understood 3-manifolds are Haken 3-manifolds; these are manifolds that are irreducible and contain incompressible surfaces. One approach to 3-manifolds is to try to generalize the notion of an incompressible surface. Essential laminations and mapped-in π1-injective surfaces have both been used with some success as substitutes for incompressible surfaces, yielding theorems which apply t...

A new class of compact Kähler manifolds, called special, is defined: they are the ones having no surjective meromorphic map to an orbifold of general type. The special manifolds are in many respect higher-dimensional generalisations of rational and elliptic curves. For example, we show that being rationally connected or having vanishing Kodaira dimension implies being special. For any compact K...

Given a (smooth) complex analytic family of compact complex manifolds, we prove that the central fibre must be Moishezon if the other fibres are Moishezon. Using a strongly Gauduchon metric on the central fibre whose existence was proved in our previous work on limits of projective manifolds, we show that the irreducible components of the relative Barlet space of divisors contained in the fibre...

A. Van de Ven has pointed out in connection with his recent results(1) that there are not many known examples of compact connected complex 4-manifolds with positive indices. The purpose of this note is to exhibit a series of compact connected complex 4-manfolds M . . . . n, m = 2, 3, 4, ..., with positive indices. Each complex 4-manifold Mn.m is an irregular algebraic surface having a structure...

The main purpose of this article is to describe compact orientable irreducible 3-manifolds that have a non-trivial JSJ-decomposition and 2-generated fundamental group. The rank of a group is the minimal number of elements needed to generate it. A natural question is whether the Heegaard genus of such a manifold is equal to 2. When the JSJ-decomposition is empty, there are examples of closed 3ma...