We give a local classification of generalized complex structures. About a point, a generalized complex structure is equivalent to a product of a symplectic manifold with a holomorphic Poisson manifold. We use a Nash-Moser type argument in the style of Conn’s linearization theorem.
"Local classification of generalize complex structures." J. Differential Geom. 95 (1) 1 - 37, September 2013. https://doi.org/10.4310/jdg/1375124607