On the Mumford–Tate conjecture for hyperkähler varieties

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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  • Salvatore Floccari

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OriginalspracheEnglisch
Seiten (von - bis)309-324
Seitenumfang16
FachzeitschriftManuscripta mathematica
Jahrgang168
Ausgabenummer3-4
Frühes Online-Datum25 Mai 2021
PublikationsstatusVeröffentlicht - Juli 2022

Abstract

We study the Mumford–Tate conjecture for hyperkähler varieties. We show that the full conjecture holds for all varieties deformation equivalent to either an Hilbert scheme of points on a K3 surface or to O’Grady’s ten dimensional example, and all of their self-products. For an arbitrary hyperkähler variety whose second Betti number is not 3, we prove the Mumford–Tate conjecture in every codimension under the assumption that the Künneth components in even degree of its André motive are abelian. Our results extend a theorem of André.

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On the Mumford–Tate conjecture for hyperkähler varieties. / Floccari, Salvatore.
in: Manuscripta mathematica, Jahrgang 168, Nr. 3-4, 07.2022, S. 309-324.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Floccari S. On the Mumford–Tate conjecture for hyperkähler varieties. Manuscripta mathematica. 2022 Jul;168(3-4):309-324. Epub 2021 Mai 25. doi: 10.1007/s00229-021-01316-4
Floccari, Salvatore. / On the Mumford–Tate conjecture for hyperkähler varieties. in: Manuscripta mathematica. 2022 ; Jahrgang 168, Nr. 3-4. S. 309-324.
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