Deformations of generalized complex and generalized Kahler structures

Understand

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 holomorphic Poisson structures on a Kahler manifold induce deformations of generalized Kahler structures.