Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism
Kuroda, Shigeru
Tohoku Math. J. (2), Tome 62 (2010) no. 1, p. 75-115 / Harvested from Project Euclid
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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 deduce that no tame automorphism of a polynomial ring admits a reduction of type IV.
Publié le : 2010-05-15
Classification:  Polynomial automorphisms,  tame generators problem,  14R10,  13F20 
@article{1270041028,
     author = {Kuroda, Shigeru},
     title = {Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism},
     journal = {Tohoku Math. J. (2)},
     volume = {62},
     number = {1},
     year = {2010},
     pages = { 75-115},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1270041028}
}

Kuroda, Shigeru. Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism. Tohoku Math. J. (2), Tome 62 (2010) no. 1, pp.  75-115. http://gdmltest.u-ga.fr/item/1270041028/