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.

Published Feb. 1, 2019 1:10 PM - Last modified Apr. 4, 2020 8:54 PM