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 structures parametrized by the global sections of a certain line bundle on X. This generalizes to the case of framed vector bundles previous results obtained by the author 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 \cup \{\infty\} admit a natural holomorphic symplectic structure.