Sixfolds of generalized Kummer type and K3 surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909061888344064 |
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| author | Floccari, Salvatore |
| author_facet | Floccari, Salvatore |
| contents | We prove that any hyper-Kähler 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02948 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sixfolds of generalized Kummer type and K3 surfaces Floccari, Salvatore Algebraic Geometry We prove that any hyper-Kähler 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. |
| title | Sixfolds of generalized Kummer type and K3 surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2210.02948 |