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Derived equivalences of hyperkähler varieties

Date: Thursday, March 5, 2020 13:30 - 15:30
Speaker: Lenny Taelman (Universiteit van Amsterdam)
Location: Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Tamas Hausel

In this talk we consider auto-equivalences of the bounded derived category D(X) of coherent sheaves on a smooth projective complex variety X. By a result of Orlov, any such auto-equivalence induces an (ungraded) automorphism of the singular cohomology H(X,\Q). If X is a K3 surface, then work of Mukai, Orlov, Huybrechts, Macr and Stellari completely describes the image of the map \rho_X : \Aut D(X) --> Aut(H(X, \Q)). We will study the image of \rho_X for higher-dimensional hyperkhler varieties. An important tool is a certain Lie algebra acting on H(X, \Q), introduced by Verbitsky, Looijenga and Lunts. We show that this Lie algebra is a derived invariant, and use this to study the image of \rho_X.
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