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THE INTEGRAL HODGE CONJECTURE FOR 3-FOLDS OF KODAIRA DIMENSION ZERO
Part of
Burt Totaro
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

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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.

Foliations with radial Kupka set and pencils of Calabi–Yau hypersurfaces
Omegar Calvo-Andrade, Luís Gustavo Mendes, Ivan Pan
Journal:

Compositio Mathematica / Volume 142 / Issue 6 / November 2006

Published online by Cambridge University Press:

24 November 2006, pp. 1587-1593

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November 2006
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We show that holomorphic singular codimension one foliations of the complex projective space with a Kupka singular set of radial type and verifying some global hypotheses have rational first integral. The generic elements of such pencils are Calabi–Yau.

Some Calabi–Yau threefolds with obstructed deformations over the Witt vectors
Stefan Schröer
Journal:

Compositio Mathematica / Volume 140 / Issue 6 / November 2004

Published online by Cambridge University Press:

15 October 2004, pp. 1579-1592

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November 2004
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Some smooth Calabi–Yau threefolds in characteristic two and three that do not lift to characteristic zero are constructed. These threefolds are pencils of supersingular K3-surfaces. The construction depends on Moret-Bailly's pencil of abelian surfaces and Katsura's analysis of generalized Kummer surfaces. The threefold in characteristic two turns out to be nonrigid.

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THE INTEGRAL HODGE CONJECTURE FOR 3-FOLDS OF KODAIRA DIMENSION ZERO

Foliations with radial Kupka set and pencils of Calabi–Yau hypersurfaces

Some Calabi–Yau threefolds with obstructed deformations over the Witt vectors