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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?

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# Symplectic but Not Complex Manifolds.

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