On the Chow ring of certain algebraic hyper-Kähler manifolds

C. Voisin (1)

1 IMJ - Institut de Mathématiques de Jussieu

We study a generalization of a conjecture made by Beauville on the Chow ring of hyper-Kähler algebraic varieties. Namely we prove in a number of cases that polynomial cohomological relations involving only CH^1(X) and the Chern classes of X are satisfied in CH(X). These cases are : punctual Hilbert schemes of a K3 surface S parameterizing subschemes of length n, for n<2b_2(S)_tr+5; Fano varieties of lines in a cubic fourfold.

Mots clés: Chow ring; Chern classes; hyper-Kähler varieties.; hyper-Kähler varieties

Domaines: Géométrie algébrique [math.AG]

C. Voisin. On the Chow ring of certain algebraic hyper-Kähler manifolds. 2007. ⟨hal-00019236v3⟩