Remarks And Questions On Coisotropic Subvarieties and 0-Cycles of Hyper-Kähler Varieties

Abstract

This paper proposes a conjectural picture for the structure of the Chow ring CH_*(X) of a (projective) hyper-Kähler variety X, that seems to emerge from the recent papers [9], [24], [25], [26], with emphasis on the Chow group CH₀(X) of 0-cycles (in this paper, Chow groups will be taken with ℚ-coefficients). Our motivation is Beauville’s conjecture (see [5]) that for such an X, the Bloch-Beilinson filtration has a natural, multiplicative, splitting.