On Parabolic Bundles on Algebraic Surfaces

The aim of this paper is to construct the parabolic version of the Gieseker-Uhlenbeck map from the Gieseker compactification of the moduli space of parabolic stable bundles to the Donaldson-Uhlenbeck compactification of the moduli space of vector bundles with parabolic structures along a divisor with normal crossing singularities on an algebraic surface.