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Finite extensions of mappings from a smooth variety

We present an example of finite mappings of algebraic varieties f : V → W, where V ⊂ k, W ⊂ k, and F : k → k such that F |V = f and gdeg F = 1 < gdeg f (gdeg h means the number of points in the generic fiber of h). Thus, in some sense, the result of this note improves our result in J. Pure Appl. Algebra 148 (2000) where it was shown that this phenomenon can occur when V ⊂ k, W ⊂ k with m ≥ n + 2. In the case V, W ⊂ k a similar example does not exist.