Unobstructed K-deformations of Generalized Complex Structures and Bihermitian Structures

Details Unobstructed K-deformations of Generalized Complex Structures and Bihermitian Structures Unobstructed K-deformations of Generalized Complex Structures and Bihermitian Structures

2009-11-16

arxiv.org/abs/0911.2958v2

Mathematics

Differential Geometry

38 pages, explanation improved, e.g., definition of bihermitian structures with the same orientation, added references

Scientific paper

We introduce K-deformations of generalized complex structures on a compact Kahler manifold $M=(X, J)$ with an effective anti-canonical divisor and show that obstructions to K-deformations of generalized complex structures on $M$ always vanish. Applying the stability theorem of generalized Kahler structures, together with unobstructed K-deformations, we construct deformations of bihermitian structures in the form $(J, J^-_t, h_t)$ on a compact Kahler surface with a non-zero holomorphic Poisson structure. Then we prove that a compact Kahler surface $S$ admits a non-trivial bihermitian structure if and only if $S$ has a non-zero holomorphic Poisson structure.

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