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Some desultory remarks concerning algebraic cycles and Calabi–Yau threefolds

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Abstract

We study some conjectures about Chow groups of varieties of geometric genus one. Some examples are given of Calabi–Yau threefolds where these conjectures can be verified, using the theory of finite-dimensional motives.

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Notes

  1. The definition of Calabi–Yau variety in [28] is different from ours, as it is not required that \(h^{2,0}=0\); however (as noted in [13, Section 4.1], the varieties \(X_{3,1}\) and \(X_{3,2}\) do have \(h^{2,0}=0\).

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Acknowledgments

The ideas developed in this note grew into being during the Strasbourg 2014—2015 groupe de travail based on the monograph [46]. Thanks to all the participants of this groupe de travail for a pleasant and stimulating atmosphere. Thanks to Charles Vial for interesting email correspondence, and to Bert van Geemen for informing me about the Beauville threefold and providing the reference [13]. Thanks to the referee for helpful remarks on a prior version. Many thanks to Yasuyo, Kai and Len for making it possible to work at home in Schiltigheim.

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  1. CNRS-IRMA, Université de Strasbourg, 7 rue René Descartes, 67084, Strasbourg cedex, France

    Robert Laterveer

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Laterveer, R. Some desultory remarks concerning algebraic cycles and Calabi–Yau threefolds. Rend. Circ. Mat. Palermo, II. Ser 65, 333–344 (2016). https://doi.org/10.1007/s12215-016-0237-y

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