Under numerical assumptions, connected components of moduli spaces of modular vector bundles on K3^{[n]}-type IHS manifolds are again IHS manifolds of K3^{[n]}-type and induce derived equivalences with the original manifolds.
Bottini, O'Grady's tenfolds from stable bundles on hyper-Kähler fourfolds, Preprint, arXiv:2411.18528 https://arxiv.org/abs/2411.18528
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Lecture notes summarizing recent progress on hyper-Kähler varieties via Lagrangian fibrations, atomic sheaves, and derived categories.
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Hyper-K\"ahler varieties: Lagrangian fibrations, atomic sheaves, and categories
Lecture notes summarizing recent progress on hyper-Kähler varieties via Lagrangian fibrations, atomic sheaves, and derived categories.