A twisted derived category of K3^[n]-type hyper-Kähler varieties is governed by the oriented Markman-Mukai lattice, proven under a primitivity condition and yielding derived equivalences between fine K3 moduli spaces of the same dimension.
Every rational Hodge isometry between two K3 surfaces is algebraic
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A twisted derived category of hyper-K\"ahler varieties of $K3^{[n]}$-type
A twisted derived category of K3^[n]-type hyper-Kähler varieties is governed by the oriented Markman-Mukai lattice, proven under a primitivity condition and yielding derived equivalences between fine K3 moduli spaces of the same dimension.