Chern classes in Deligne cohomology for coherent analytic sheaves

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.

Minor changes

References in corpus (3)

• Autour de la cohomologie de Bott-Chern
• Geometry of Deligne cohomology
• A counterexample to the Hodge conjecture for Kaehler varieties

Cited by in corpus (7)

• Mayer-Vietoris systems and their applications
• Leray-Hirsch theorem and blow-up formula for Dolbeault cohomology
• D-bar Spark Theory and Deligne Cohomology
• Coherent sheaves, superconnections, and RRG
• Vector bundles on proper toric 3-folds and certain other schemes
• Variation of the holomorphic determinant bundle
• Chern currents of coherent sheaves