A pencil of Enriques surfaces with non-algebraic integral Hodge classes

2019/06/21 by Ottem, John Christian, Suzuki, Fumiaki · 1 citation
#14C25 #14C30 #14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.08994

Abstract

We prove that there exists a pencil of Enriques surfaces defined over ℚ with non-algebraic integral Hodge classes of non-torsion type. This gives the first example of a threefold with the trivial Chow group of zero-cycles on which the integral Hodge conjecture fails. As an application, we construct a fourfold which gives the negative answer to a classical question of Murre on the universality of the Abel-Jacobi maps in codimension three.

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• Varieties with representable CH₀-group and a question of Colliot-Thélène

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