Deformations of generalized complex and generalized Kahler structures

Details Deformations of generalized complex and generalized Kahler structures Deformations of generalized complex and generalized Kahler structures

2007-05-17

arxiv.org/abs/0705.2495v3

J.Differential Geometry, vol 84,No.3, 2010,525-560

Mathematics

Differential Geometry

36 pages, minor changes, To appear in Journal of Differential Geometry

Scientific paper

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.

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