Chow--Kuenneth decomposition for special varieties

Details Chow--Kuenneth decomposition for special varieties Chow--Kuenneth decomposition for special varieties

2007-10-22

arxiv.org/abs/0710.4002v1

Mathematics

Algebraic Geometry

Scientific paper

In this paper we investigate Murre's conjecture on the Chow--K\"unneth 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--K\"unneth 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--K\"unneth decompositions.

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