Finite morphism
Finite map (algebraic geometry); Finite type scheme
In algebraic geometry, a finite morphism between two affine varieties X, Y is a dense regular map which induces isomorphic inclusion k\left[Y\right]\hookrightarrow k\left[X\right] between their coordinate rings, such that k\left[X\right] is integral over k\left[Y\right]. This definition can be extended to the quasi-projective varieties, such that a regular map f\colon X\to Y between quasiprojective varieties is finite if any point like y\in Y has an affine neighbourhood V such that U=f^{-1}(V) is affine and f\colon U\to V is a finite map (in view of the previous definition, because it is between affine varieties).