Geometric degree of finite extensions of mappings from a smooth variety

Let f:V→W be a finite polynomial mapping of algebraic subsets V,W of image and image, respectively, with n≤m. It is known that f can be extended to a finite polynomial mapping image. Moreover, it is known that, if V,W are smooth of dimension k,4k+2≤n=m, and f is dominated on every component (without vertical components) then there exists a finite polynomial extension image such that image, where image means the number of points in the generic fiber of h. In this note we improve this result. Namely we show that there exists a finite polynomial extension image such that image.