Is there any theorem characterizing those sypmlectic manifolds that can be embedded symplectically in projective space equipped with FubiniStudy symplectic form?
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According to this paper: http://arxiv.org/pdf/math/9811167.pdf, it is a theorem of Gromov and Tischler (op cit) that EVERY compact symplectic manifold is a symplectic submanifold of complex projective space. 

