Relative Chow-Kuenneth decompositions for morphisms of threefolds

Details Relative Chow-Kuenneth decompositions for morphisms of threefolds Relative Chow-Kuenneth decompositions for morphisms of threefolds

2009-11-18

arxiv.org/abs/0911.3639v4

Mathematics

Algebraic Geometry

20 pages

Scientific paper

We show that any nonconstant morphism of a threefold admits a relative Chow-Kuenneth decomposition. As a corollary we get sufficient conditions for threefolds to admit an absolute Chow-Kuenneth decomposition. In case the image of the morphism is a surface, this implies another proof of a theorem on the absolute Chow-Kuenneth 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.

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