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On integral Hodge classes on uniruled or Calabi-Yau threefolds

If X is a smooth projective complex threefold, the Hodge conjecture holds for degree 4 rational Hodge classes on X. Kollar gave examples where it does not hold for integral Hodge classes of degree 4, that is integral Hodge classes need not be classes of algebraic 1-cycles with integral coefficients. We show however that the Hodge conjecture holds for integral Hodge classes of degree 4 on a uniruled or a Calabi-Yau threefold.

preprint2004arXivOpen access
Claire Voisin
math.AG
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Claire Voisin

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