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Article Dans Une Revue Commentarii Mathematici Helvetici Année : 2020

Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero

Résumé

We prove that the product of an Enriques surface and a very general curve of genus at least 1 does not satisfy the integral Hodge conjecture for 1-cycles. This provides the first examples of smooth projective complex threefolds of Kodaira dimension zero for which the integral Hodge conjecture fails, and the first examples of non-algebraic torsion cohomology classes of degree 4 on smooth projective complex threefolds.

Dates et versions

hal-02358000 , version 1 (11-11-2019)

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Olivier Benoist, John Christian Ottem. Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero. Commentarii Mathematici Helvetici, 2020, 95 (1), pp.27-35. ⟨10.4171/CMH/479⟩. ⟨hal-02358000⟩
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