Two explorations in symplectic geometry

Abstract

In Part I we study the moduli space of holomorphic parabolic vector bundles over a curve, using combinatorial techniques to obtain information about the structure of the cohomology ring. We consider the ring generated by the Chern classes of tautological line bundles on the moduli space of parabolic bundles of arbitrary rank on a Riemann surface. We show the Poincaré duals to these Chern classes have simple geometric representatives, and use this construction to show that the ring generated by these Chern classes vanishes below the dimension of the moduli space, in analogy with the Newstead-Ramanan conjecture for stable bundles.