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arXiv · 1802.01845

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

Olivier Benoist·John Christian Ottem
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Abstract

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.

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Olivier Benoist, John Christian Ottem. 2018-02-06. Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero. https://doi.org/10.4171/cmh/479

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