Poisson structures on moduli spaces of parabolic bundles on surfaces

Let X be a smooth complex projective surface and D an effective divisor on X such that H-0(X, omega (-1)(X) (-D)) not equal 0. Let us denote by PB the moduli space of stable parabolic vector bundles on X with parabolic struct ure over the divisor D (with fixed weights and Hilbert polynomials). We pro ve that the moduli space PB is a non-singular quasi-projective variety natu rally endowed with a family of holomorphic Poisson structures parametrized by the global sections of omega (-1)(X) (-D). This result is the natural ge neralization to the moduli spaces of parabolic vector bundles of the result s obtained in [B2] for the moduli spaces of stable sheaves on a Poisson sur face. We also give, in some special cases, a detailed description of the sy mplectic leaf foliation of the Poisson manifold PB.