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Abstract des Vortrages von Malte Wandel

Induced automorphisms on manifolds of K3^[n]-type

I will report on a recent joint work with Giovanni Mongardi concerning certain automorphisms on manifolds that are deformation equivalent to hilbert schemes of points on a K3. I will present a numerical, that is, lattice theoretical criterion how to identify whether a given manifold is, in fact, a moduli space of stable objects on a K3 surface and a given automorphism of this manifold is, in fact, induced by an automorphism of the surface. This criterion will then be applied to the classification of prime order non-symplectic automorphisms of manifolds of K3^[2]-type. If time permits, I will conclude with an outlook on certain approaches to study automorphisms of O'Grady's manifolds.