Poincaré and Picard bundles on the moduli spaces of bundles on curves

Abstract

Poincare bundles and Picard bundles on the Jacobian of a smooth curve have been studied extensively classically. Peter Newstead and his collaborators have made major contributions to the theory of Poincaré and Picard bundles over the moduli spaces of vector bundles of higher ranks. We present old and new results on the Poincare bundles and Picard bundles on the moduli spaces of vector bundles on smooth curves and their generalisations to nodal curves. Finally we consider parabolic vector bundles. We prove the parabolic stability of Poincaré bundles over the moduli spaces of parabolic vector bundles, with parabolic structure of any type, on a smooth curve.