Mathematische Annalen

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

Chern classes in Deligne cohomology for coherent analytic sheaves

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.

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© Springer-Verlag 2009

Authors and Affiliations

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

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