Poisson structures on moduli spaces of framed vector bundles on surfaces

In this paper we prove that the moduli spaces of framed vector bundles over a surface X, satisfying certain conditions, admit a family of Poisson stru ctures parametrized by the global sections of a certain line bundle on X. T his generalizes to the case of framed vector bundles previous results obtai ned in [B2] for the moduli space of vector bundles over a Poisson surface. As a corollary of this result we prove that the moduli spaces of framed SU( r)-instantons on S-4 = R-4 boolean OR {infinity }admit a natural holomorphi c symplectic structure.