The Chern character of a parabolic bundle, and a parabolic Reznikov theorem in the case of finite order at infinity

Jaya Iyer (1, 2) , Carlos Simpson (3)

1 IMSc - Institute of Mathematical Sciences [Chennai]
2 School of Mathematics [Princeton]
3 JAD - Laboratoire Jean Alexandre Dieudonné

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 $\geq 2$.

Domaines: Géométrie algébrique [math.AG]

Jaya Iyer, Carlos Simpson. The Chern character of a parabolic bundle, and a parabolic Reznikov theorem in the case of finite order at infinity. 2006. ⟨hal-00118656v1⟩