# Fishy version of Kodaira embedding theorem !

Is there any theorem characterizing those sypmlectic manifolds that can be embedded symplectically in projective space equipped with Fubini-Study symplectic form?

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Why is this community wiki? –  Igor Rivin Feb 26 '12 at 6:15
You should also see this mathoverflow question: mathoverflow.net/questions/59733/… –  Sam Lisi Feb 26 '12 at 11:07
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## 1 Answer

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.

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(Every compact symplectic manifold with integral symplectic class, that is.) –  Tim Perutz Feb 26 '12 at 17:28
Thanks Tim, what about the symplectic orbifolds. I mean is there an embedding theorem for them in some suitable weighted progective spaces? –  Hamed Aug 8 at 19:10
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