Kähler–de Rham Cohomology and Chern Classes

Abstract

Constraints on the Chern classes of a vector bundle on a possibly singular algebraic variety are found, which are stronger than the obvious Hodge theoretic constraints. This is done by showing that these lift to Chern classes in the hypercohomology of the complex of Kähler differentials.

Key Words:

• Chern classes
• de Rham filtration
• Hodge filtration
• Kähler–de Rham cohomology

2000 Mathematics Subject Classification:

• 14F43
• 14C30

ACKNOWLEDGMENT

The first author was partially supported by the NSF. Second author supported by PIMS postdoctoral fellowship and the University of Alberta.

Notes

Communicated by C. Pedrini.