Abstract

We show that any nonconstant morphism of a threefold admits a relative Chow–Künneth decomposition. As a corollary we get sufficient conditions for threefolds to admit an absolute Chow–Künneth decomposition. In case the image of the morphism is a surface, this implies another proof of a theorem on the absolute Chow–Künneth decomposition for threefolds satisfying a certain condition, which was obtained by the first author with P. L. del Angel. In case the image is a curve, this improves in the threefold case a theorem obtained by the second author where the singularity of the morphism was assumed isolated and the condition on the general fiber was stronger.