Deformations of generalized complex and generalized Kahler structures
Deformations of generalized complex and generalized Kahler structures
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DOI：
10.4310/jdg/1279114300
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发表时间：
2007-05
影响因子：
2.5
通讯作者：
R. Goto
中科院分区：
文献类型：
--
作者：
R. Goto
本文得到了广义复杂结构在小变形作用下单纯旋量广义Kahler结构的稳定性定理。(这类似于Kodaira-Spencer的Kahler流形的稳定性定理。)我们将稳定性定理应用于一类允许变形到广义复流形的紧致Kahler流形，得到了Fano曲面和Toric Kahler流形上的非平凡广义Kahler结构。特别地，我们证明了Kahler流形上的全纯Poisson结构导致了广义Kahler结构的变形。
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.