Let $S$ be a K3 surface over $\mathbb{C}$, that is, $S$ is a simply connected compact smooth complex surface whose canonical bundle is trivial. I recall reading somewhere that any two such surfaces are diffeomorphic, however I can't for the life of me remember where, or how the proof goes. 


Does anybody know a good reference to a proof, or can provide a proof?


Thanks,
Dan



Are any two K3 surfaces over C diffeomorphic?
I think this was first proved by Kodaira. See [On the structure of complex analytic surfaces, 1](http://www.jstor.org/pss/2373157). There Kodaira proves that any K3 surface is a deformation of a non-singular quartic surface in $\mathbb{CP}^3$. In particular, they are all diffeomorphic.


