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THE INTEGRAL HODGE CONJECTURE FOR 3-FOLDS OF KODAIRA DIMENSION ZERO
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 5 / September 2021
- Published online by Cambridge University Press:
- 18 February 2020, pp. 1697-1717
- Print publication:
- September 2021
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We prove the integral Hodge conjecture for all 3-folds
$X$ of Kodaira dimension zero with 
$H^{0}(X,K_{X})$ not zero. This generalizes earlier results of Voisin and Grabowski. The assumption is sharp, in view of counterexamples by Benoist and Ottem. We also prove similar results on the integral Tate conjecture. For example, the integral Tate conjecture holds for abelian 3-folds in any characteristic.
The curve exclusion theorem for elliptic and K3 fibrations birational to Fano 3-fold hypersurfaces
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 1 / February 2009
- Published online by Cambridge University Press:
- 02 February 2009, pp. 189-210
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