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

Marek Karaś, and Jakub Zygadło. "Wild Multidegrees of the Form (d,d₂,d₃) for Fixed d ≥ 3." Bulletin of the Polish Academy of Sciences. Mathematics 60.3 (2012): 211-218. <http://eudml.org/doc/281166>.

@article{MarekKaraś2012,
abstract = {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.},
author = {Marek Karaś, Jakub Zygadło},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {polynomial automorphism; wild automorphism, multidegree},
language = {eng},
number = {3},
pages = {211-218},
title = {Wild Multidegrees of the Form (d,d₂,d₃) for Fixed d ≥ 3},
url = {http://eudml.org/doc/281166},
volume = {60},
year = {2012},
}

TY - JOUR
AU - Marek Karaś
AU - Jakub Zygadło
TI - Wild Multidegrees of the Form (d,d₂,d₃) for Fixed d ≥ 3
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2012
VL - 60
IS - 3
SP - 211
EP - 218
AB - 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.
LA - eng
KW - polynomial automorphism; wild automorphism, multidegree
UR - http://eudml.org/doc/281166
ER -