Derived equivalences between hyperkähler varieties

We study equivalences D(X)–>D(Y) between the derived categories of coherent sheaves on complex hyperkähler varieties X and Y. An important tool is the Looijenga–Lunts–Verbitsky Lie algebra acting on the total cohomology of X. We show that this Lie algebra is preserved by derived equivalences, and deduce various consequences from this.
Based on arXiv:1906.08081.