| Starting with a K3 surface with an automorphism of finite order, it is rather easy to produce automorphisms on (some) of its moduli spaces of stable sheaves. In this talk we give an answer to the converse: when is a manifold a moduli space of sheaves on a K3 and when are its automorphisms induced from those of the surface? Time permitting, we will discuss related results on lagrangian fibrations. This is joint work with Malte Wandel. |