Sixfolds of generalized Kummer type and K3 surfaces

authored by

Salvatore Floccari

Abstract

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

Organisation(s)

Institute of Algebraic Geometry

Type

Article

Journal

Compositio mathematica

Volume

160

Pages

388-410

No. of pages

23

ISSN

0010-437x

Publication date

02.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory

Electronic version(s)

https://doi.org/10.48550/arXiv.2210.02948 (Access: Open)
https://doi.org/10.1112/S0010437X23007625 (Access: Open)
https://doi.org/10.15488/16792 (Access: Open)