DEFORMATIONS OF GENERALIZED COMPLEX AND GENERALIZED KAHLER STRUCTURES

In this paper we obtain a stability theorem of generalized Kahler structures with one pure spinor under small deformations of generalized complex structures. (This is analogous to the stability theorem of Kahler manifolds by Kodaira-Spencer.) We apply the stability theorem to a class of compact Kahler manifolds which admits deformations to generalized complex manifolds and obtain non-trivial generalized Kahler structures on Fano surfaces and toric Kahler manifolds. In particular, we show that every nonzero holomorphic Poisson structure on a Kahler manifold induces deformations of non-trivial generalized Kahler structures.