Some examples of 1-convex non-embeddable threefolds
  We construct a family of 1-convex threefolds, with exceptional curve C of type (0,-2), which are not embeddable in C^m \times CP_n. In order to show that they are not Kaehler we exhibit a real 3-dimensional chain A whose boundary is the complex curve C. 
Giovanni Bassanelli, Marco Leoni