Geometric degree of finite extensions of mappings from a smooth variety |
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Authors: | Marek Kara? |
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Institution: | Instytut Matematyki, Uniwersytetu Jagiellońskiego, ul. Reymonta 4, 30-059 Kraków, Poland |
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Abstract: | Let f:V→W be a finite polynomial mapping of algebraic subsets V,W of and , respectively, with n≤m. It is known that f can be extended to a finite polynomial mapping . 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 such that , where 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 such that . |
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Keywords: | 14Rxx 14R10 |
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