Polynomial mappings with small degree

Let Xn be an affine variety of dimension n and Yn be a quasi-projective variety of the same dimension. We prove that for a quasi-finite polynomial mapping f : Xn → Yn ,every non-empty component of the set Yn\f(Xn) is closed and it has dimension greater or equal to (…), where (…) is a geometric degree of f. Moreover, we prove that generally, if (…) is any polynomial mapping, then either every non-empty component of the set (…) is of dimension (…) or f contracts a subvariety of dimension (…).