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arXiv · 2203.16257

On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties

Salvatore Floccari
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Abstract

We prove that the rational Chow motive of a six dimensional hyper-K\"{a}hler 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-K\"{a}hler varieties of OG6-type.

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Salvatore Floccari. 2022-03-30. On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties. https://doi.org/10.46298/epiga.2022.9758

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