Journal of the Mathematical Society of Japan

A family of cubic fourfolds with finite-dimensional motive


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We prove that cubic fourfolds in a certain 10-dimensional family have finite-dimensional motive. The proof is based on the van Geemen–Izadi construction of an algebraic Kuga–Satake correspondence for these cubic fourfolds, combined with Voisin’s method of “spread”. Some consequences are given.

Article information

J. Math. Soc. Japan, Volume 70, Number 4 (2018), 1453-1473.

Received: 1 March 2016
Revised: 9 April 2017
First available in Project Euclid: 27 July 2018

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Zentralblatt MATH identifier

Primary: 14C15: (Equivariant) Chow groups and rings; motives 14C25: Algebraic cycles 14C30: Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture
Secondary: 14K99: None of the above, but in this section

algebraic cycles Chow groups motives finite-dimensional motives cubic fourfolds abelian varieties Kuga–Satake correspondence


LATERVEER, Robert. A family of cubic fourfolds with finite-dimensional motive. J. Math. Soc. Japan 70 (2018), no. 4, 1453--1473. doi:10.2969/jmsj/74497449.

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