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

Abstract : 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 $\geq 2$.
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Preprints, Working Papers, ...

Cited literature [28 references]

https://hal.archives-ouvertes.fr/hal-00118656
Contributor : Carlos Simpson <>
Submitted on : Friday, February 2, 2007 - 5:12:02 PM
Last modification on : Monday, August 19, 2019 - 4:20:06 PM
Long-term archiving on: Tuesday, September 21, 2010 - 12:34:12 PM

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### Citation

Jaya Iyer, Carlos Simpson. The Chern character of a parabolic bundle, and a parabolic Reznikov theorem in the case of finite order at infinity. 2007. ⟨hal-00118656v2⟩

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