Relative Chow-Kuenneth decompositions for morphisms of threefolds

Stefan Müller-Stach; Morihiko Saito

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arXiv · 0911.3639

Relative Chow-Kuenneth decompositions for morphisms of threefolds

Stefan Müller-Stach·Morihiko Saito

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Abstract

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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BibTeX RIS

Stefan Müller-Stach, Morihiko Saito. 2009-11-18. Relative Chow-Kuenneth decompositions for morphisms of threefolds. https://arxiv.org/abs/0911.3639

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