Automorphisms of a Polynomial Ring Which Admit Reductions of Type I

作者：Kuroda Shigeru^*

来源：Publications of the Research Institute for Mathematical Sciences, 2009, 45(3): 907-917.

DOI：10.2977/prims/1249478968

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.

• 出版日期2009-8