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.

10 pages; final version, published in EPIGA

References in corpus (3)

• Induced Automorphisms on Irreducible Symplectic Manifolds
• Algebraic cycles on a generalized Kummer variety
• Supersingular O'Grady varieties of dimension six