C∞-logarithmic transformations and generalized complex structures

We show that there are generalized complex structures on all 4-manifolds obtained by logarithmic transformations with arbitrary multiplicity along symplectic tori with trivial normal bundle. Applying a technique of broken Lefschetz fibrations, we obtain generalized complex structures with arbitrary large numbers of connected components of type changing loci on every manifold which is obtained from a symplectic 4-manifold by a logarithmic transformation of multiplicity 0 along a symplectic torus with trivial normal bundle. Elliptic surfaces with non-zero euler characteristic and the connected sums (2m-1) S-2 x S-2, (2m-1) CP2#(lCP) over bar (2) and S-1 x S-3 admit twisted generalized complex structures J(n) with n type changing loci for arbitrary large n.