Generalized complex structure: Difference between revisions

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===Local holomorphicity===

Near non-regular points, the above classification theorem does not apply. However, about any point, a generalized complex manifoldismanifold is, up to diffeomorphism and B-field, a product of a symplectic manifold with a generalized complex manifold which is of complex type at the point, much like Weinstein's theorem for the local structure of [[Poisson manifold]]s. The remaining question of the local structure is: what does a generalized complex structure look like near a point of complex type? In fact, it will be induced by a holomorphic [[Poisson manifold|Poisson structure]].

==Examples==