On the motive of O'Grady's six-dimensional hyper-Kähler varieties

Abstract

We prove that the rational Chow motive of a six-dimensional hyper-Kähler variety obtained as symplectic resolution of O'Grady type of a singular moduli space of semistable sheaves on an Abelian surface A belongs to the tensor category of motives generated by the motive of A. We in fact give a formula for the rational Chow motive of such a variety in terms of that of the surface. As a consequence, the conjectures of Hodge and Tate hold for many hyper-Kähler varieties of OG6-type.