On the Chow ring of certain algebraic hyper-Kähler manifolds

Abstract

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.

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

References in corpus (3)

• On the Cobordism Class of the Hilbert Scheme of a Surface
• Mukai implies McKay: the McKay correspondence as an equivalence of derived categories
• The cup product of the Hilbert scheme for K3 surfaces

Cited by in corpus (6)

• Chow rings and decomposition theorems for families of K3 surfaces and Calabi-Yau hypersurfaces
• The Chow ring of double EPW sextics
• On the Chow motive of an abelian scheme with non-trivial endomorphisms
• Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi-Yau complete intersections
• Some remarks on modified diagonals
• Smooth Surfaces in Smooth Fourfolds with Vanishing First Chern Class