Let X n be an affine variety of dimension n and Y n be a quasi-projective variety of the same dimension. We prove that for a quasi-finite polynomial mapping ƒ : X n → Y n , every non-empty component of the set Y n ƒ (X n ) is closed and it has dimension greater or equal to n μ(ƒ), where μ(ƒ) is a geometric degree of ƒ. Moreover, we prove that generally, if ƒ : X n → Y n is any polynomial mapping, then either every non-empty component of the set is of dimension ≥ n μ(ƒ) or ƒ contracts a subvariety of dimension ≥ n μ(ƒ) + 1.
展开▼
