Sixfolds of generalized Kummer type and K3 surfaces

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

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  • Salvatore Floccari

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OriginalspracheEnglisch
Seiten (von - bis)388-410
Seitenumfang23
FachzeitschriftCompositio mathematica
Jahrgang160
Ausgabenummer2
Frühes Online-Datum5 Jan. 2024
PublikationsstatusVeröffentlicht - Feb. 2024

Abstract

We prove that any hyper-Kähler sixfold K of generalized Kummer type has a naturally associated manifold YK of K3[3] type. It is obtained as crepant resolution of the quotient of K by a group of symplectic involutions acting trivially on its second cohomology. When K is projective, the variety YK is birational to a moduli space of stable sheaves on a uniquely determined projective K3 surface SK. As an application of this construction we show that the Kuga–Satake correspondence is algebraic for the K3 surfaces SK, producing infinitely many new families of K3 surfaces of general Picard rank 16 satisfying the Kuga–Satake Hodge conjecture.

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Sixfolds of generalized Kummer type and K3 surfaces. / Floccari, Salvatore.
in: Compositio mathematica, Jahrgang 160, Nr. 2, 02.2024, S. 388-410.

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

Floccari S. Sixfolds of generalized Kummer type and K3 surfaces. Compositio mathematica. 2024 Feb;160(2):388-410. Epub 2024 Jan 5. doi: 10.48550/arXiv.2210.02948, 10.1112/S0010437X23007625, 10.15488/16792
Floccari, Salvatore. / Sixfolds of generalized Kummer type and K3 surfaces. in: Compositio mathematica. 2024 ; Jahrgang 160, Nr. 2. S. 388-410.
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