Differential forms on moduli spaces of parabolic bundles

Let X be a smooth projective variety, and let PB be a moduli space of stable parabolic bundles on X. For any flat family E_* of parabolic bundles on X parametrized by a smooth scheme Y, and for any integer m, with 1 <= m <= dim X, we construct a closed differential form \Omega = \Omega_{E_*} on Y with values in H^m(X, O_X). By using the vector-valued differential form \Omega we then prove that, for any i >= 0, the choice of a (non-zero) element \sigma \in H^i(X, \Omega^{i+m}_X), determines, in a natural way, a closed differential m-form \Omega_{\sigma} on the smooth locus of PB.