On the motive of O'Grady's six dimensional hyper-Kähler varieties
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866908862554046464 |
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| author | Floccari, Salvatore |
| author_facet | Floccari, Salvatore |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_16257 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the motive of O'Grady's six dimensional hyper-Kähler varieties Floccari, Salvatore Algebraic Geometry 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. |
| title | On the motive of O'Grady's six dimensional hyper-Kähler varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2203.16257 |