Deformations of generalized complex and generalized Kahler structures
Differential Geometry
2010-09-21 v3
Abstract
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.
Cite
@article{arxiv.0705.2495,
title = {Deformations of generalized complex and generalized Kahler structures},
author = {Ryushi Goto},
journal= {arXiv preprint arXiv:0705.2495},
year = {2010}
}