Derived categories of generalized Kummer varieties: extended Mukai vector
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908600628150272 |
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| author | Yang, Yuxuan |
| author_facet | Yang, Yuxuan |
| contents | We use the extended Mukai vectors for hyper-Kähler manifolds to investigate the derived equivalences of the hyper-Kähler manifolds which are deformation equivalent to generalized Kummer varieties. Inspired by the idea for hyper-Kähler manifolds of $\mathrm{K3}^{[n]}$-type, we obtain an integral lattice which is proved to be invariant under the derived equivalences of generalized Kummer type varieties. Such results and applications are described using derived monodromy groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16279 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derived categories of generalized Kummer varieties: extended Mukai vector Yang, Yuxuan Algebraic Geometry 14J42 We use the extended Mukai vectors for hyper-Kähler manifolds to investigate the derived equivalences of the hyper-Kähler manifolds which are deformation equivalent to generalized Kummer varieties. Inspired by the idea for hyper-Kähler manifolds of $\mathrm{K3}^{[n]}$-type, we obtain an integral lattice which is proved to be invariant under the derived equivalences of generalized Kummer type varieties. Such results and applications are described using derived monodromy groups. |
| title | Derived categories of generalized Kummer varieties: extended Mukai vector |
| topic | Algebraic Geometry 14J42 |
| url | https://arxiv.org/abs/2510.16279 |