Moduli space of parabolic vector bundles on a curve

Let X be an irreducible smooth complex projective curve. Faltings gave a cohomological criterion for vector bundles on X to be semistable. Using this criterion he gave a construction of the moduli spaces of vector bundles on X (Faltings in J Alg Geom 2:507–568, 1993). An analogous cohomological criterion for semistable parabolic vector bundles on X is now known. Our aim here is to give a construction of the moduli spaces of parabolic vector bundles using this criterion.