Chow--Kuenneth decomposition for special varieties

Abstract

In this paper we investigate Murre's conjecture on the Chow--Künneth decomposition for two classes of examples. We look at the universal families of smooth curves over spaces which dominate the moduli space $\cM_g$, in genus at most 8 and show existence of a Chow--Künneth decomposition. The second class of examples include the representation varieties of a finitely generated group with one relation. This is done in the setting of equivariant cohomology and equivariant Chow groups to get equivariant Chow--Künneth decompositions.

References in corpus (3)

• Chow-Kunneth decomposition for universal families over Picard modular surfaces
• Chow-Kunneth decomposition for varieties with low cohomological level
• Künneth projectors for open varieties