A Note on Geometric Degree of Finite Extensions of Mappings from a Smooth Variety

• Autorzy: Marek Karaś
• Języki publikacji: EN

Abstrakty

EN

Let f:V → W be a finite polynomial mapping of algebraic subsets V,W of kⁿ and $k^{m}$, respectively, with n ≤ m. Kwieciński [J. Pure Appl. Algebra 76 (1991)] proved that there exists a finite polynomial mapping $F:kⁿ → k^{m}$ such that $F|_{V} = f$. In this note we prove that, if V,W ⊂ kⁿ are smooth of dimension k with 3k+2 ≤ n, and f:V → W is finite, dominated and dominated on every component, then there exists a finite polynomial mapping F: kⁿ → kⁿ$ such that $F|_{V} = f$ and $gdeg F ≤ (gdeg f)^{k+1}$. This improves earlier results of the author.

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: 2008
• Tom: 56
• Numer: 2
• Strony: 105-108

Daty

wydano

2008

Twórcy

autor

Marek Karaś

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

Identyfikatory

DOI

10.4064/ba56-2-2