Geodesic
On the universal CH$_ 0$ group of cubic hypersurfaces
Journal of the European Mathematical Society, Tome 19 (2017) no. 6, pp. 1619-1653.

Voir la notice de l'article provenant de la source EMS Press

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 θ4/4! 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.
DOI : 10.4171/jems/702
Classification : 14-XX
Keywords: Cubic hypersurfaces, decomposition of the diagonal, stable rationality 
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     author = {Claire Voisin},
     title = {On the universal {CH}$_ 0$  group of cubic hypersurfaces},
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Claire Voisin. On the universal CH$_ 0$  group of cubic hypersurfaces. Journal of the European Mathematical Society, Tome 19 (2017) no. 6, pp. 1619-1653. doi : 10.4171/jems/702. http://geodesic.mathdoc.fr/articles/10.4171/jems/702/

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