A ug 2 00 7 Automorphisms of a polynomial ring which admit reductions of type I
نویسنده
چکیده
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.
منابع مشابه
Automorphisms of a polynomial ring which admit reductions of type I Shigeru Kuroda
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 t...
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