On the universal CH0 group of cubic hypersurfaces
نویسنده
چکیده
We study the existence of a Chow-theoretic decomposition of the diagonal of a smooth cubic hypersurface, or equivalently, the universal triviality of its CH0-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 X, this turns out to be equivalent to the algebraicity of the minimal class θ/4! of the intermediate Jacobian J(X). In dimension 4, we show that a special cubic fourfold with discriminant not divisible by 4 has universally trivial CH0 group.
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