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Comparison of the Beilinson-Chern Classes With the Chern-Cheeger-Simons Classes

  • Jean-Luc Brylinski
Part of the Progress in Mathematics book series (PM, volume 172)

Abstract

The Chern-Cheeger-Simons (CCS) classes of a vector bundle with connection belong to the group ofdifferential characters of[Chee-S], and depend on the choice of a connection. For a projective complex manifold, we introduce a smaller group, the group ofrestricted differential characters, which contains the CCS classes of holomorphic vector bundles equipped with a connection compatible with the complex structure.We construct a map from this group to a Deligne cohomology group, and show that unintroduce logarithmic resticted differential character as a receptacle of the CCS classes for algebraic vector bundles equipped with a connection with logarithmic singularities, and related the CCS classes to the Beilinson-Chern classes in the logarithmic context. From this we deduce that for a flat vector bundleEover a quasi-projective algebraic manifoldX, the Beilinson-Chern classes given are the images of the Chern-Cheeger-Simons classes under some canonical map(thereby extending results of Bloch [BI] and Soulé[S]).

Keywords

Exact Sequence Vector Bundle Line Bundle Chern Class Holomorphic Vector Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Jean-Luc Brylinski
    • 1
  1. 1.Department of MathematicsPenn State UniversityUniversity ParkUSA

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