\(p\)-Conjecture for tame automorphisms of \(\mathbb{C}^3\)
The famous Jung-van der Kulk [4, 11] theorem says that any polynomial automorphism of \(\mathbb{C}^2\) can be decomposed into a finite number of affine automorphisms and triangular automorphisms, i.e. that any polynomial automorphism of \(\mathbb{C}^2\) is a tame automorphism. In [5] there is a conj...
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| Дата: | 2025 |
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Lugansk National Taras Shevchenko University
2025
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-23492025-04-13T15:32:01Z \(p\)-Conjecture for tame automorphisms of \(\mathbb{C}^3\) Holik, Daria Karaś, Marek polynomial automorphism, tame automorphism, wild automorphism, multidegree 14Rxx, 14R10, 16W20 The famous Jung-van der Kulk [4, 11] theorem says that any polynomial automorphism of \(\mathbb{C}^2\) can be decomposed into a finite number of affine automorphisms and triangular automorphisms, i.e. that any polynomial automorphism of \(\mathbb{C}^2\) is a tame automorphism. In [5] there is a conjecture saying that for any tame automorphism of \(\mathbb{C}^3,\) if \((p,d_2,d_3)\) is a multidegree of this automorphism, where \(p\) is a prime number and \(p\leq d_2\leq d_3,\) then \(p|d_2\) or \(d_3\in p\mathbb{N}+d_2\mathbb{N}.\) Up to now this conjecture is unsolved. In this note, we study this conjecture and give some results that are partial results in the direction of solving the conjecture. We also give some complimentary results. Lugansk National Taras Shevchenko University 2025-04-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2349 10.12958/adm2349 Algebra and Discrete Mathematics; Vol 39, No 1 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2349/pdf Copyright (c) 2025 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2025-04-13T15:32:01Z |
| collection |
OJS |
| language |
English |
| topic |
polynomial automorphism tame automorphism wild automorphism multidegree 14Rxx 14R10 16W20 |
| spellingShingle |
polynomial automorphism tame automorphism wild automorphism multidegree 14Rxx 14R10 16W20 Holik, Daria Karaś, Marek \(p\)-Conjecture for tame automorphisms of \(\mathbb{C}^3\) |
| topic_facet |
polynomial automorphism tame automorphism wild automorphism multidegree 14Rxx 14R10 16W20 |
| format |
Article |
| author |
Holik, Daria Karaś, Marek |
| author_facet |
Holik, Daria Karaś, Marek |
| author_sort |
Holik, Daria |
| title |
\(p\)-Conjecture for tame automorphisms of \(\mathbb{C}^3\) |
| title_short |
\(p\)-Conjecture for tame automorphisms of \(\mathbb{C}^3\) |
| title_full |
\(p\)-Conjecture for tame automorphisms of \(\mathbb{C}^3\) |
| title_fullStr |
\(p\)-Conjecture for tame automorphisms of \(\mathbb{C}^3\) |
| title_full_unstemmed |
\(p\)-Conjecture for tame automorphisms of \(\mathbb{C}^3\) |
| title_sort |
\(p\)-conjecture for tame automorphisms of \(\mathbb{c}^3\) |
| description |
The famous Jung-van der Kulk [4, 11] theorem says that any polynomial automorphism of \(\mathbb{C}^2\) can be decomposed into a finite number of affine automorphisms and triangular automorphisms, i.e. that any polynomial automorphism of \(\mathbb{C}^2\) is a tame automorphism. In [5] there is a conjecture saying that for any tame automorphism of \(\mathbb{C}^3,\) if \((p,d_2,d_3)\) is a multidegree of this automorphism, where \(p\) is a prime number and \(p\leq d_2\leq d_3,\) then \(p|d_2\) or \(d_3\in p\mathbb{N}+d_2\mathbb{N}.\) Up to now this conjecture is unsolved. In this note, we study this conjecture and give some results that are partial results in the direction of solving the conjecture. We also give some complimentary results. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2025 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2349 |
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2025-07-17T10:36:21Z |
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2025-07-17T10:36:21Z |
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