Theorem of existence and completeness for holomorphic Poisson structures

In this paper, we define a concept of a family of compact holomorphic Poisson manifolds on the basis of Kodaira-Spencer’s deformation theory and deduce the integrability condition. We prove an analogue of their Theorem of existence for complex analytic structures' under some analytic assumption, and establish an analogue of their Theorem of completeness for complex analytic structures’ in the context of holomorphic Poisson deformations.