The set of points at which a morphism of affine schemes is not finite
Assume that $X,Y$ are integral noetherian affine schemes. Let $f:X\rightarrow Y$ be a dominant, generically finite morphism of finite type. We show that the set of points at which the morphism $f$ is not finite is either empty or a hypersurface. An example is given to show that this is no longer true in the non-noetherian case.