Deformations of generalized complex and generalized Kahler structures

Ryushi Goto

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arXiv · 0705.2495

Deformations of generalized complex and generalized Kahler structures

Ryushi Goto

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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.

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BibTeX RIS

Ryushi Goto. 2009-11-17. Deformations of generalized complex and generalized Kahler structures. https://arxiv.org/abs/0705.2495

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