Chow-Künneth decomposition for some moduli spaces

Abstract

In this paper we investigate Murre's conjecture on the Chow–Künneth decomposition for universal families of smooth curves over spaces which dominate the moduli space ${\mathcal{M}}_g$, in genus at most 8 and show existence of a Chow–Künneth decomposition. This is done in the setting of equivariant cohomology and equivariant Chow groups to get equivariant Chow–Künneth decompositions.