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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 Ω = Ω E * on Y with values in H m (X, O X ). By using the vector-valued differential form Ω we then prove that the choice of a (non-zero) differential m-form σ on X, σ ∈ H 0 (X, Ω m X ), determines, in a natural way, a closeddoi:10.1216/rmj-2010-40-6-1779 fatcat:rv66m2hqyze2dgfmq2q5nlzsvq