Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism
Commutative Algebra
2008-10-14 v2 Algebraic Geometry
Abstract
In 2003, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of a polynomial ring. In the present paper, we reconstruct their theory by using the "generalized Shestakov-Umirbaev inequality", which was recently given by the author. As a consequence, we obtain a more precise tameness criterion for polynomial automorphisms. In particular, we show that no tame automorphism of a polynomial ring admits a reduction of type IV.
Keywords
Cite
@article{arxiv.0801.0117,
title = {Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism},
author = {Shigeru Kuroda},
journal= {arXiv preprint arXiv:0801.0117},
year = {2008}
}
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52 pages