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Mathematische Annalen

, Volume 347, Issue 2, pp 249–284 | Cite as

Chern classes in Deligne cohomology for coherent analytic sheaves

  • Julien GrivauxEmail author
Article

Abstract

In this article, we construct Chern classes in rational Deligne cohomology for coherent sheaves on a smooth complex compact manifold. We prove that these classes satisfy the functoriality property under pullbacks, the Whitney formula and the Grothendieck–Riemann–Roch theorem for projective morphisms between smooth complex compact manifolds.

Keywords

Exact Sequence Chern Class Cohomology Ring Free Resolution 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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© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Université Pierre et Marie CurieParis Cedex 05France

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