On the universal CH group of cubic hypersurfaces
Claire Voisin
Collège de France, Paris, France
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Abstract
We study the existence of a Chow-theoretic decomposition of the diagonal of a smooth cubic hypersurface, or equivalently, the universal triviality of its CH group. We prove that for odd-dimensional cubic hypersurfaces or for cubic fourfolds, this is equivalent to the existence of a cohomological decomposition of the diagonal, and we translate geometrically this last condition. For cubic threefolds , this turns out to be equivalent to the algebraicity of the minimal class of the intermediate Jacobian . In dimension 4, we show that a special cubic fourfold with discriminant not divisible by 4 has universally trivial CH group.
Cite this article
Claire Voisin, On the universal CH group of cubic hypersurfaces. J. Eur. Math. Soc. 19 (2017), no. 6, pp. 1619–1653
DOI 10.4171/JEMS/702