On the Chow ring of certain algebraic hyper-Kähler manifolds

Details On the Chow ring of certain algebraic hyper-Kähler manifolds On the Chow ring of certain algebraic hyper-Kähler manifolds

2006-02-18

arxiv.org/abs/math/0602400v3

Mathematics

Algebraic Geometry

Final version. To appear in PAMQ, volume in honour of Bogomolov

Scientific paper

We study a generalization of a conjecture made by Beauville on the Chow ring of hyper-K\"ahler 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.

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