In this paper, we obtain an explicit formula for the Chern character of a
locally abelian parabolic bundle in terms of its constituent bundles. Several
features and variants of parabolic structures are discussed. Parabolic bundles
arising from logarithmic connections form an important class of examples. As an
application, we consider the situation when the local monodromies are
semi-simple and are of finite order at infinity. In this case the parabolic
Chern classes of the associated locally abelian parabolic bundle are deduced to
be zero in the rational Deligne cohomology in degrees ≥2.Comment: Adds and corrects reference