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arXiv · 2510.16279

Derived categories of generalized Kummer varieties: extended Mukai vector

Yuxuan Yang
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Abstract

We use the extended Mukai vectors for hyper-K\"ahler manifolds to investigate the derived equivalences of the hyper-K\"ahler manifolds which are deformation equivalent to generalized Kummer varieties. Inspired by the idea for hyper-K\"ahler 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.

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Yuxuan Yang. 2025-10-18. Derived categories of generalized Kummer varieties: extended Mukai vector. https://arxiv.org/abs/2510.16279

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