Sixfolds of generalized Kummer type and K3 surfaces

Salvatore Floccari

doi:10.48550/arXiv.2210.02948

Details

Original language	English
Pages (from-to)	388-410
Number of pages	23
Journal	Compositio Mathematica
Volume	160
Issue number	2
Early online date	5 Jan 2024
Publication status	Published - Feb 2024

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.

Keywords

math.AG, Hodge conjecture, hyper-Kähler varieties, K3 surfaces

ASJC Scopus subject areas

Mathematics(all)
Algebra and Number Theory

Cite this

Sixfolds of generalized Kummer type and K3 surfaces. / Floccari, Salvatore.
In: Compositio Mathematica, Vol. 160, No. 2, 02.2024, p. 388-410.

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

Floccari, S 2024, 'Sixfolds of generalized Kummer type and K3 surfaces', Compositio Mathematica, vol. 160, no. 2, pp. 388-410. https://doi.org/10.48550/arXiv.2210.02948, https://doi.org/10.1112/S0010437X23007625, https://doi.org/10.15488/16792

Floccari, S. (2024). Sixfolds of generalized Kummer type and K3 surfaces. Compositio Mathematica, 160(2), 388-410. https://doi.org/10.48550/arXiv.2210.02948, https://doi.org/10.1112/S0010437X23007625, https://doi.org/10.15488/16792

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 ; Vol. 160, No. 2. pp. 388-410.

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