The smooth center of the cohomology of a singular variety

TL;DR

This paper investigates the constraints on Chern classes of vector bundles on singular varieties and explores the existence of Hodge cycles not expressible as linear combinations of these classes.

Contribution

It introduces new constraints on Chern classes for vector bundles on singular varieties and analyzes Hodge cycles outside the span of these classes.

Findings

Identifies limitations on Chern classes in singular settings

Shows existence of Hodge cycles not generated by Chern classes

Provides new tools for studying vector bundles on singular varieties

Abstract

We study constraints on the Chern classes of a vector bundle on a singular variety. We use this constraint to study a variety which carries a Hodge cycle that are not a linear combination of Chern classes of vector bundles on it.