Deformation in holomorphic Poisson manifolds

In this paper, we consider deforming a coisotropic submanifold Y   in a holomorphic Poisson manifold (X,π)(X,π). Under the assumption that Y has a holomorphic tubular neighborhood, we associate Y   with an L∞L∞-algebra that controls the deformations of Y  . This L∞L∞-algebra can also be extended to control the simultaneous deformations of the holomorphic Poisson structure π and the coisotropic submanifold Y.