On the Chow ring of certain algebraic hyper-K\"ahler manifolds
Algebraic Geometry
2011-11-09 v3
Abstract
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.
Cite
@article{arxiv.math/0602400,
title = {On the Chow ring of certain algebraic hyper-K\"ahler manifolds},
author = {C. Voisin},
journal= {arXiv preprint arXiv:math/0602400},
year = {2011}
}
Comments
Final version. To appear in PAMQ, volume in honour of Bogomolov