Instantons, Poisson structures and generalized Kahler geometry

Using the idea of a generalized Kahler structure, we construct bihermitian metrics on CP2 and CP1 x CP1, and show that any such structure on a compact 4-manifold M defines one on the moduli space of anti-self-dual connections on a fixed principal bundle over M. We highlight the role of holomorphic Poisson structures in all these constructions.