Unobstructed K-deformations of Generalized Complex Structures and Bihermitian Structures

Ryushi Goto

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arXiv · 0911.2958

Unobstructed K-deformations of Generalized Complex Structures and Bihermitian Structures

Ryushi Goto

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Abstract

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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BibTeX RIS

Ryushi Goto. 2009-11-16. Unobstructed K-deformations of Generalized Complex Structures and Bihermitian Structures. https://arxiv.org/abs/0911.2958

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