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.
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Constructs irreducible symplectic varieties of dimension 2n (2≤n≤10) with 16≤b2≤24 as non-trivial terminalisations of finite symplectic quotients of Beauville-Mukai systems on very general K3-del Pezzo double covers.
Lecture notes summarizing recent progress on hyper-Kähler varieties via Lagrangian fibrations, atomic sheaves, and derived categories.
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On moduli spaces of vector bundles on $K3^{[n]}$-type IHS manifolds
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.
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Irreducible symplectic varieties via K3-del Pezzo double covers
Constructs irreducible symplectic varieties of dimension 2n (2≤n≤10) with 16≤b2≤24 as non-trivial terminalisations of finite symplectic quotients of Beauville-Mukai systems on very general K3-del Pezzo double covers.
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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.