On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties
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...
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| Format: | Article |
| Language: | English |
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Association Epiga
2023-02-01
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| Series: | Épijournal de Géométrie Algébrique |
| Subjects: | |
| Online Access: | https://epiga.episciences.org/9758/pdf |
| _version_ | 1827311455349768192 |
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| author | Salvatore Floccari |
| author_facet | Salvatore Floccari |
| author_sort | Salvatore Floccari |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T20:19:12Z |
| format | Article |
| id | doaj.art-20414711049340b4bb9e16904597ee53 |
| institution | Directory Open Access Journal |
| issn | 2491-6765 |
| language | English |
| last_indexed | 2024-04-24T20:19:12Z |
| publishDate | 2023-02-01 |
| publisher | Association Epiga |
| record_format | Article |
| series | Épijournal de Géométrie Algébrique |
| spelling | doaj.art-20414711049340b4bb9e16904597ee532024-03-22T09:12:47ZengAssociation EpigaÉpijournal de Géométrie Algébrique2491-67652023-02-01Volume 710.46298/epiga.2022.97589758On the motive of O'Grady's six dimensional hyper-K\"{a}hler varietiesSalvatore Floccarihttps://orcid.org/0000-0002-9954-5937We 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.https://epiga.episciences.org/9758/pdfmathematics - algebraic geometry |
| spellingShingle | Salvatore Floccari On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties Épijournal de Géométrie Algébrique mathematics - algebraic geometry |
| title | On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties |
| title_full | On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties |
| title_fullStr | On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties |
| title_full_unstemmed | On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties |
| title_short | On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties |
| title_sort | on the motive of o grady s six dimensional hyper k a hler varieties |
| topic | mathematics - algebraic geometry |
| url | https://epiga.episciences.org/9758/pdf |
| work_keys_str_mv | AT salvatorefloccari onthemotiveofogradyssixdimensionalhyperkahlervarieties |