Journal of the Mathematical Society of Japan

A family of cubic fourfolds with finite-dimensional motive

Robert LATERVEER

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1532678875

Digital Object Identifier
doi:10.2969/jmsj/74497449

Mathematical Reviews number (MathSciNet)
MR3868213

Zentralblatt MATH identifier
07009708

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.jmsj/1532678875


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