Yuxuan Yang (UMass). Derived categories of generalized Kummer varieties: extended Mukai vector

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 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. The talk is based on the paper arXiv:2510.16279.