| In this talk, I will describe holomorphic Poisson manifolds, Lie algebroids and Lie groupoids from the viewpoint of real Poisson geometry. I will give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri-Morosi and describe a double complex which computes the holomorphic Poisson cohomology. To that purpose, I will show that a holomorphic Lie algebroid structure is equivalent to a matched pair of complex Lie algebroids in the sense of Lu. I will also say a few words on the integrability of
holomorphic Lie algebroids. |
