Let $X$ and $Y$ be K3 surfaces over an algebraically closed field of characteristic 0. Is it possible to have a dominant morphism $X\to Y$ which is not an isomorphism?
In positive characteristic, the Frobenius and its iterates give examples of dominant morphisms between K3 surfaces which are not isomorphisms. Are there any others?
Comment: there are many examples (in any characteristic) of dominant rational maps $X\dashrightarrow Y$ between K3 surfaces, and also many examples of nontrivial automorphisms of K3 surfaces.
If $f:X\to Y$ was such a map, it is unramified since $K_X,K_Y$ are trivial. So,it is finite and thus an etale covering. But these are simply connected and thus it must be an isomorphism.