On the motive of O'Grady's six dimensional hyper-Kähler varieties

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Authors

  • Salvatore Floccari

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Original languageEnglish
Article numberA4
JournalEpijournal de Geometrie Algebrique
Volume7
Issue number7
Publication statusPublished - 13 Feb 2023

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.

Keywords

    Hodge conjecture, Hyper-Kähler varieties, moduli spaces, motives

ASJC Scopus subject areas

Cite this

On the motive of O'Grady's six dimensional hyper-Kähler varieties. / Floccari, Salvatore.
In: Epijournal de Geometrie Algebrique, Vol. 7, No. 7, A4, 13.02.2023.

Research output: Contribution to journal › Article › Research › peer review

Floccari, S 2023, 'On the motive of O'Grady's six dimensional hyper-Kähler varieties', Epijournal de Geometrie Algebrique, vol. 7, no. 7, A4. https://doi.org/10.46298/epiga.2022.9758
Floccari, S. (2023). On the motive of O'Grady's six dimensional hyper-Kähler varieties. Epijournal de Geometrie Algebrique, 7(7), Article A4. https://doi.org/10.46298/epiga.2022.9758
Floccari S. On the motive of O'Grady's six dimensional hyper-Kähler varieties. Epijournal de Geometrie Algebrique. 2023 Feb 13;7(7):A4. doi: 10.46298/epiga.2022.9758
Floccari, Salvatore. / On the motive of O'Grady's six dimensional hyper-Kähler varieties. In: Epijournal de Geometrie Algebrique. 2023 ; Vol. 7, No. 7.
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