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

2020 ◽  
Vol 95 (1) ◽  
pp. 27-35
Author(s):  
Olivier Benoist ◽  
John Christian Ottem
Keyword(s):  
Kodaira Dimension ◽  
Hodge Conjecture ◽  
Dimension Zero

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

2020 ◽  
pp. 1-21
Author(s):  
Burt Totaro
Keyword(s):  
Kodaira Dimension ◽  
Hodge Conjecture ◽  
Dimension Zero ◽  
Tate Conjecture

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.

scholarly journals Halphen pencils on weighted Fano threefold hypersurfaces

2009 ◽  
Vol 7 (1) ◽  
pp. 1-45 ◽  
Author(s):  
Ivan Cheltsov ◽  
Jihun Park
Keyword(s):  
Kodaira Dimension ◽  
Dimension Zero ◽  
Fano Threefold

AbstractOn a general quasismooth well-formed weighted hypersurface of degree Σi=14 a i in ℙ(1, a 1, a 2, a 3, a 4), we classify all pencils whose general members are surfaces of Kodaira dimension zero.

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