CHOW GROUPS, CHOW COHOMOLOGY, AND LINEAR VARIETIES

Abstract

We compute the Chow groups and the Fulton–MacPherson operational Chow cohomology ring for a class of singular rational varieties including toric varieties. The computation is closely related to the weight filtration on the ordinary cohomology of these varieties. We use the computation to answer one of the open problems about operational Chow cohomology: it does not have a natural map to ordinary cohomology.

Keywords

• 14C15 (primary)
• 14F42
• 14M20 (secondary)