STABLE PARABOLIC BUNDLES AND FLAT SINGULAR CONNECTIONS

Let X be a Riemann surface, E --> X a holomorphic vector bundle with parabolic structure over the points P(i) is-an-element-of X; we construct spaces of connections on E, singular at the points P(i), which "represent" the parabolic structure; we then use Donaldson's method to give a differential-geometric proof of a theorem of Mehta and Seshadri about stable parabolic vector bundles.