Deformations of generalized complex and generalized kahler structures

Ryushi Goto Osaka University

Differential Geometry mathscidoc:1609.10172

Journal of Differential Geometry, 84, (3), 525-560, 2010
In this paper we obtain a stability theorem of generalized K¨ahler structures with one pure spinor under small deformations of generalized complex structures. (This is analogous to the stability theorem of K¨ahler manifolds by Kodaira-Spencer.) We apply the stability theorem to a class of compact K¨ahler manifolds which admits deformations to generalized complex manifolds and obtain non-trivial generalized K¨ahler structures on Fano surfaces and toric K¨ahler manifolds. In particular, we show that every nonzero holomorphic Poisson structure on a K¨ahler manifold induces deformations of non-trivial generalized K¨ahler structures.
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@inproceedings{ryushi2010deformations,
  title={DEFORMATIONS OF GENERALIZED COMPLEX AND GENERALIZED KAHLER STRUCTURES},
  author={Ryushi Goto},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911213824959607829},
  booktitle={Journal of Differential Geometry},
  volume={84},
  number={3},
  pages={525-560},
  year={2010},
}
Ryushi Goto. DEFORMATIONS OF GENERALIZED COMPLEX AND GENERALIZED KAHLER STRUCTURES. 2010. Vol. 84. In Journal of Differential Geometry. pp.525-560. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911213824959607829.
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