Moishezon manifolds whose Picard group is of rank one

In this paper, we use Mori theory to analyze the structure of Moishezon manifolds with Picard group equal to Z, with big canonical bundle, and which become projective after one blow-up. In this context, we study the Mori contraction on the projective model, and we show that in general the center of the blow-up has <<low>> codimension. In dimension 3, the canonical bundle is nef by a result of Kollar. We show that this result is no longer true in dimension 4 or larger than 4 by constructing explicitly some examples, which give also new Moishezon manifolds not satisfying the Demailly-Siu criterion. In dimension 4, we show that the center of the blow-up is a surface, and that our construction is the only possible one when the canonical bundle is not nef; in particular, the center of the blow-up must be P-2 in this last case.