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Wild Multidegrees of the Form (d,d₂,d₃) for Fixed d ≥ 3

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Karaś M., Zygadło J.

Bulletin of the Polish Academy of Sciences. Mathematics

2012

tom 60

nr 3

211-218

Let d be any integer greater than or equal to 3. We show that the intersection of the set mdeg(Aut(ℂ³))∖ mdeg(Tame(ℂ³)) with {(d₁,d₂,d₃) ∈ (ℕ ₊)³: d = d₁ ≤ d₂≤ d₃} has infinitely many elements, where mdeg h = (deg h₁,...,deg hₙ) denotes the multidegree of a polynomial mapping h = (h₁,...,hₙ): ℂⁿ → ℂⁿ. In other words, we show that there are infinitely many wild multidegrees of the form (d,d₂,d₃), with fixed d ≥ 3 and d ≤ d₂ ≤ d₃, where a sequence (d₁,...,dₙ)∈ ℕ ⁿ is a wild multidegree if there is a polynomial automorphism F of ℂⁿ with mdeg F = (d₁,...,dₙ), and there is no tame automorphism of ℂⁿ with the same multidegree.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Karaś M.

1 Zygadło J.

1 2012

Wyniki wyszukiwania

Wild Multidegrees of the Form (d,d₂,d₃) for Fixed d ≥ 3