On the universal $CH_0$ group of cubic hypersurfaces

By Claire Voisin. 2014

71 citations recorded by the source corpus.

We study the existence of a Chow-theoretic decomposition of the diagonal of a smooth cubic hypersurface, or equivalently, the universal triviality of its ${\rm CH}_0$-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 $\theta^4/4!$ 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 ${\rm CH}_0$ group.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/55fc2481b3d292120c385e5aaacc4bace23a03f1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. M. Shen
2. L. Fu
3. Charles Vial
4. Robert Laterveer

In Mathematical Physics

1. M. Shen
2. L. Fu
3. Charles Vial
4. Robert Laterveer

Citations in the corpus

• The generalized Franchetta conjecture for some hyper-Kähler varieties, II (2020, methodology): “Our starting point is the isomorphism of Chow motives (26) which can be obtained by applying the blow-up formula and the projective bundle formula for Chow motives to the construction due to Galkin–Shinder [GS14] and Voisin [Voi17]; see [ –”