Automorphisms of a polynomial ring which admit reductions of type I

Simple item page
dc.creatorKuroda, Shigeru
dc.date2007-08-16
dc.date2007-09-10
dc.date.accessioned2026-07-07T08:28:06Z
dc.date.available2026-07-07T08:28:06Z
dc.descriptionRecently, 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.
dc.descriptionQuestion 4.1 of the first version was answered
dc.identifierhttps://arxiv.org/abs/0708.2120
dc.identifierhttp://arxiv.org/abs/0708.2120
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137496
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject14R10; 13N15; 14R20
dc.titleAutomorphisms of a polynomial ring which admit reductions of type I
dc.typetext

Files

Collections

arXiv