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

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...

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Bibliographic Details
Published in:Mathematische annalen 2020-06, Vol.377 (1-2), p.183-197
Main Authors: Ottem, John Christian, Suzuki, Fumiaki
Format: Article
Language:English
Subjects:
Algebra
Integrals
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-020-01969-8