Unobstructed K-deformations of Generalized Complex Structures and Bihermitian Structures

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.

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

References in corpus (4)

• Symmetries in generalized Kähler geometry
• Generalized Kahler geometry and manifest N=(2,2) supersymmetric nonlinear sigma-models
• Anti-self-dual bihermitian structures on Inoue surfaces
• Deformations of Generalized Kahler Structures and Bihermitian Structures

Cited by in corpus (4)

• Generalized Kahler geometry
• Twistors and Bi-Hermitian Surfaces of Non-Kähler Type
• Moduli spaces of Einstein-Hermitian generalized connections over generalized Kahler manifolds of symplectic type
• Matsushima-Lichnerowicz type theorems of Lie algebra of automorphisms of generalized Kähler manifolds of symplectic type