Automorphisms of a polynomial ring which admit reductions of type I

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Recently, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of a polynomial ring. To solve the conjecture, they defined notions called reductions of types I--IV for automorphisms of a polynomial ring. An automorphism admitting a reduction of type I was first found by Shestakov-Umirbaev. Using a computer, van den Essen--Makar-Limanov--Willems gave a family of such automorphisms. In this paper, we present a new construction of such automorphisms using locally nilpotent derivations. As a consequence, we discover that there exists an automorphism admitting a reduction of type I which satisfies some degree condition for each possible value.
Question 4.1 of the first version was answered

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Commutative Algebra, Algebraic Geometry, 14R10; 13N15; 14R20

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http://salesiana.dossiersoluciones.com/handle/123456789/137496

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.2120
 http://arxiv.org/abs/0708.2120

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arXiv