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

  • Olivier Benoist

    École Normale Supérieure, Paris, France
  • John Christian Ottem

    University of Oslo, Norway
Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero cover
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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.

Cite this article

Olivier Benoist, John Christian Ottem, Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero. Comment. Math. Helv. 95 (2020), no. 1, pp. 27–35

DOI 10.4171/CMH/479