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We present an example of finite mappings of algebraic varieties ƒ : V → W, where V ⊂ kn, W ⊂ kn+1, and F : kn → kn+1 such that F¦v = ƒ and gdeg F = 1 < gdeg/ (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 ⊂ kn, W ⊂ km with...
Let ƒ : V → W be a finite polynomial mapping of algebraic subsets V, W of k[sup]n and k[sup]m, respectively, with n ≤ m. Kwieciński [J. Pure Appl. Algebra 76 (1991)] proved that there exists a finite polynomial mapping F : k[sup]n → k[sup]m such that F| v = ƒ. In this note we prove that, if V, W ⊂ k[sup] are smooth of dimension k with 3k + 2 ≤ n, and ƒ : V → W is finite, dominated and dominated on...
In this note we prove that for every finite sets V, W [is a subset of] [C^k] with k, #V, #W > 1 and for every surjective mapping f : V --> W there exists a finite mapping F : [C^k] --> [C^k] such that F\v = f, gdegF = gdegf and degF [is less than or equal to (#V - 1)^2].
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