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Apr 13, 2011 at 10:44 answer added Eigenbunny timeline score: 1
Mar 27, 2011 at 21:12 comment added Dmitri Panov If you are happy with just an opinion, it looks to me that both question might be open. I would think, that the answer to 1 should be positive, i.e., there should be a conter-example, a 4-dimensional symplectic non-Kahler submanifold in $\mathbb CP^4$. The only positive statement for questions of this type that I know, is that it is expected that a symplectic surface in $CP^2$ is symplecticly isotopic to an aglebraic curve.
Mar 27, 2011 at 15:52 history asked Yunhyung Cho CC BY-SA 2.5