  We first extend the notion of connection in the context of Courant algebroids
to obtain a new characterization of generalized Kaehler geometry. We then
establish a new notion of isomorphism between holomorphic Poisson manifolds,
which is non-holomorphic in nature. Finally we show an equivalence between
certain configurations of branes on Poisson varieties and generalized Kaehler
structures, and use this to construct explicitly new families of generalized
Kaehler structures on compact holomorphic Poisson manifolds equipped with
positive Poisson line bundles (e.g. Fano manifolds). We end with some
speculations concerning the connection to non-commutative algebraic geometry.
