\(p\)-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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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2025
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2349 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
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