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Some cubics with finite-dimensional motive

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Abstract

This small note presents in any dimension a family of cubics that have finite-dimensional motive (in the sense of Kimura). As an illustration, we verify a conjecture of Voevodsky for these cubics and a conjecture of Murre for the Fano variety of lines of these cubics.

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Acknowledgements

This note is a belated echo of the Strasbourg 2014-2015 groupe de travail based on the monograph [35]. Thanks to all the participants for the pleasant and stimulating atmosphere. Many thanks to Yasuyo, Kai, and Len for lots of enjoyable after-work apéritifs.

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

    Robert Laterveer

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  1. Robert Laterveer
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Correspondence to Robert Laterveer.

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Laterveer, R. Some cubics with finite-dimensional motive. Bol. Soc. Mat. Mex. 24, 319–327 (2018). https://doi.org/10.1007/s40590-017-0173-7

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