# Georg Oberdieck (University of Bonn): Automorphisms of Hilbert scheme of point of surfaces

**Abstract: ****If X is a K3 surface, then the Hilbert scheme of n points on it X[n] is a hyper-Kahler manifold. Every automorphism of the K3 surface induces an automorphism of X[n]. However, there are more automorphism on X[n] and the theory of automorphisms of X[n] is a rich and beautiful subject in its own right. The talk will be concerned with the question what happens if we drop the condition on X to be a K3 surface. Do we still get interesting automorphisms of X[n] that do not come from the underlying surface? We will discuss some positive and some negative results to this question. Joint work with Pieter Belmans and Chiara Camere.**