Quantization of Holomorphic Poisson structure --related to Generalized   K\"{a}hler structure--
  It is known that holomorphic Poisson structures are closely related to theories of generalized K\"{a}hler geometry and bi-Hermitian structures. In this article, we introduce quantization of holomorphic Poisson structures which are closely related to generalized K\"{a}hler structures /bi-Hermitian structures. By resulting noncommutative product $\star$ obtained via quantization, we also demonstrate computations with respect to concrete examples. 
Naoya Miyazaki
math.DG