Abstract
This note is about the Chow groups of a certain family of smooth cubic fourfolds. This family is characterized by the property that each cubic fourfold X in the family has an involution such that the induced involution on the Fano variety F of lines in X is symplectic and has a K3 surface S in the fixed locus. The main result establishes a relation between X and S on the level of Chow motives. As a consequence, we can prove finite-dimensionality of the motive of certain members of the family.
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Acknowledgements
Thanks to all participants of the Strasbourg 2014/2015 “groupe de travail” based on the monograph [36] for a very pleasant atmosphere. Thanks to the referees for helpful comments. Many thanks to Kai and Len and Yoyo for stimulating discussions not related to this work.
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Laterveer, R. On the Chow groups of certain cubic fourfolds. Acta. Math. Sin.-English Ser. 33, 887–898 (2017). https://doi.org/10.1007/s10114-017-6477-8
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DOI: https://doi.org/10.1007/s10114-017-6477-8
Keywords
- Algebraic cycles
- Chow groups
- motives
- cubic fourfolds
- hyperkähler varieties
- K3 surfaces
- finite-dimensional motive