Non-trivial smooth families of K3 surfaces

Abstract

Let X be a complex K3 surface, $$\textrm{Diff}(X)$$ the group of diffeomorphisms of X and $$\textrm{Diff}_0(X)$$ the identity component. We prove that the fundamental group of $$\textrm{Diff}_0(X)$$ contains a free abelian group of countably infinite rank as a direct summand. The summand is detected using families Seiberg–Witten invariants. The moduli space of Einstein metrics on X is used as a key ingredient in the proof.