Hi, All: AFAIK, every complex manifold can be given a symplectic structure, by using w:=dz/\dz^ , where dz^ is the conjugate of dz, i.e., this form is closed, and symplectic. Still, I think the opposite is not true, i.e., not every symplectic manifold can be given a complex structure. Does anyone know of examples/results? I heard something about an equivalence between Lefschetz fibrations (or pencils) and existence of symplectic structures, but I cannot think of examples. Any Ideas?