Chern classes in Deligne cohomology for coherent analytic sheaves

TL;DR

This paper constructs Chern classes in rational Deligne cohomology for coherent sheaves on smooth complex compact manifolds, establishing key properties like functoriality, Whitney formula, and Grothendieck-Riemann-Roch theorem.

Contribution

It introduces a new construction of Chern classes in Deligne cohomology for coherent sheaves, extending classical theories to a broader context.

Findings

Chern classes satisfy functoriality under pullbacks

They obey the Whitney formula

They verify the Grothendieck-Riemann-Roch theorem

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 verify the functoriality property under pullbacks, the Whitney formula and the Grothendieck-Riemann-Roch theorem for projective morphisms between smooth complex compact manifolds.