Differential forms on moduli spaces of parabolic bundles

Francesco Bottacin
2010 Rocky Mountain Journal of Mathematics  
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 closed
more » ... l way, a closed differential m-form Ω σ on the smooth locus of PB.
doi:10.1216/rmj-2010-40-6-1779 fatcat:rv66m2hqyze2dgfmq2q5nlzsvq