Birational finite extensions of mappings from a smooth variety

• Autorzy: Karaś M.
• Języki publikacji: EN

Abstrakty

EN

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 m ≥ n + 2. In the case V, W ⊂ kn a similar example does not exist.

Słowa kluczowe

EN

finite mapping; birational mapping; geometric degree

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 2
• Strony: 117--120
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Karaś M.

• Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, 30-059 Kraków, Poland,

Bibliografia

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• [5] M. Karaś, Birational finite extensions, J. Pure Appl. Algebra 148 (2000), 251-253.
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• [8] M. Karaś, Geometric degree of finite extensions of mappings from a smooth variety, 3. Pure Appl. Algebra 212 (2008), 1145-1148.
• [9] M. Karaś, A note on geometric degree of finite extensions of mappings from a smooth variety, Bull. Polish Acad. Sci. Math. 56 (2008), 105-108.
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