Tame automorphisms of C³ with multidegree of the form (p₁, p₂, d₃)

• Autorzy: Karaś M.
• Języki publikacji: EN

Abstrakty

EN

Let d₃ ≥ p₂ > p₁ ≥ 3 be integers such that p₁, p₂ are prime numbers. We show that the sequence (p₁, p₂, d₃) is the multidegree of some tame automorphism of C³ if and only if d₃ ∈ p₁N p₂N, i.e. if and only if d₃ is a linear combination of p₁ and p₂ with coefficients in N.

Słowa kluczowe

EN

polynomial automorphism; tame automorphism; multidegree

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: Vol. 59, no 1
• Strony: 27--32
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Karaś M.

• Instytut Matematyki Uniwersytetu Jagiellońskiego, Łojasiewicza 6, 30-348 Kraków, Poland,

Bibliografia

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• [3] M. Karaś, There is no tame automorphism of C3 with multidegree (3,4,5), Proc. Amer. Math. Soc. 139 (2011), 769-775.
• [4] W. van der Kulk, On polynomial rings in two variables, Nieuw Arch. Wisk. (3) 1 (1953), 33-41.
• [5] I. P. Shestakov and U. U. Umirbaev, The Nagata automorphism is wild, Proc. Nat. Acad. Sci. USA 100 (2003), 12561-12563.
• [6] I. P. Shestakov, U. U. Umirbaev, The tame and the wild automorphisms of polynomial rings in three variables, J. Amer. Math. Soc. 17 (2004), 197-227.
• [7] J. Zygadło, On multidegrees of polynomial automorphisms of C3, Comm. Algebra, to appear.