Birational Finite Extensions of Mappings from a Smooth Variety

• Autorzy: Marek Karaś
• Języki publikacji: EN

Abstrakty

EN

We present an example of finite mappings of algebraic varieties f:V → W, where V ⊂ kⁿ, $W ⊂ k^{n+1}$, and $F:kⁿ → k^{n+1}$ 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, $W ⊂ k^{m}$ with m ≥ n+2. In the case V,W ⊂ kⁿ a similar example does not exist.

Kategorie tematyczne

• 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
• 14Rxx: Affine geometry

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: 57
• Numer: 2
• Strony: 117-120

Daty

wydano

2009

Twórcy

autor

Marek Karaś

• Instytut Matematyki, Uniwersytet Jagielloński, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/ba57-2-4