Birational Finite Extensions of Mappings from a Smooth Variety
Marek Karaś
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009), p. 117-120 / Harvested from The Polish Digital Mathematics Library
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We present an example of finite mappings of algebraic varieties f:V → W, where V ⊂ kⁿ, W⊂kn+1, and F:kⁿ→kn+1 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 ⊂ kⁿ, W⊂km with m ≥ n+2. In the case V,W ⊂ kⁿ a similar example does not exist.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:281135 
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     author = {Marek Kara\'s},
     title = {Birational Finite Extensions of Mappings from a Smooth Variety},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     volume = {57},
     year = {2009},
     pages = {117-120},
     zbl = {1172.14347},
     language = {en},
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Marek Karaś. Birational Finite Extensions of Mappings from a Smooth Variety. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) pp. 117-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-2-4/