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Generalized complex structures on Kodaira surfaces. (English) Zbl 1191.32006

The authors compute the deformations of the standard complex structure on a primary Kodaira surface in the space of generalized complex structures (in the sense of Hitchin). They prove that the obtained family of deformations is a smooth locally complete family depending on four complex parameters. This family is the same as the extended deformations (in the sense of Kontsevich and Barannikov) in degree two, obtained by Poon using differential Gerstenhaber algebras.

MSC:

32G05 Deformations of complex structures
32Q99 Complex manifolds
53C56 Other complex differential geometry
53D99 Symplectic geometry, contact geometry
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References:

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