Mar 5, 2020

Derived equivalences of hyperkähler varieties

Date: March 5, 2020 | 1:30 pm – 3:30 pm
Speaker: Lenny Taelman, Universiteit van Amsterdam
Location: Heinzel Seminar Room / Office Bldg West (I21.EG.101)

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.

More Information:

Date:
March 5, 2020
1:30 pm – 3:30 pm

Speaker:
Lenny Taelman, Universiteit van Amsterdam

Location:
Heinzel Seminar Room / Office Bldg West (I21.EG.101)

Contact:

OOSTHUIZEN-NOCZIL Birgit

Email:
boosthui@ist.ac.at

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