Geodesic
On the motive of O'Grady's six dimensional hyper-Kähler varieties
Épijournal de Géométrie Algébrique, Tome 7 (2023)

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We prove that the rational Chow motive of a six dimensional hyper-K"ahler 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"ahler varieties of OG6-type.
DOI : 10.46298/epiga.2022.9758
Classification : 14C15, 14C30, 14D20, 14J42 
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     author = {Floccari, Salvatore},
     title = {On the motive of {O'Grady's} six dimensional {hyper-K\"ahler} varieties},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     volume = {7},
     year = {2023},
     doi = {10.46298/epiga.2022.9758},
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Floccari, Salvatore. On the motive of O'Grady's six dimensional hyper-Kähler varieties. Épijournal de Géométrie Algébrique, Tome 7 (2023). doi: 10.46298/epiga.2022.9758

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