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arXiv · 2210.02948

Sixfolds of generalized Kummer type and K3 surfaces

Salvatore Floccari
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Abstract

We prove that any hyper-K\"{a}hler sixfold $K$ of generalized Kummer type has a naturally associated manifold $Y_K$ of $\mathrm{K}3^{[3]}$-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 $Y_K$ is birational to a moduli space of stable sheaves on a uniquely determined projective~$\mathrm{K}3$ surface~$S_K$. As application of this construction we show that the Kuga-Satake correspondence is algebraic for the K3 surfaces $S_K$, producing infinitely many new families of $\mathrm{K}3$ surfaces of general Picard rank $16$ satisfying the Kuga-Satake Hodge conjecture.

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Salvatore Floccari. 2022-10-06. Sixfolds of generalized Kummer type and K3 surfaces. https://doi.org/10.1112/s0010437x23007625

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