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Automorphismes modérés de l'espace affine

Published online by Cambridge University Press:  20 November 2018

Eric Edo
Eric Edo*
Affiliation:
Département de mathématiques pures, Université Bordeaux I, 351, cours de la Libération, 33405 Talence Cedex, FRANCE e-mail: edo@math.u-bordeaux.fr
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Résumé

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Le problème de Jung-Nagata $\left( cf.\,\left[ \text{J} \right],\,\left[ \text{N} \right] \right)$ consiste à savoir s'il existe des automorphismes de $k\left[ x,\,y,\,z \right]$ qui ne sont pas modérés. Nous proposons une approche nouvelle de cette question, fondée sur l'utilisation de la théorie des automates et du polygone de Newton. Cette approche permet notamment de généraliser de façon significative les résultats de $\left[ \text{A} \right]$.

Abstract

Abstract

The Jung-Nagata's problem $\left( cf.\,\left[ \text{J} \right],\,\left[ \text{N} \right] \right)$ asks if there exists non-tame (or wild) automorphisms of $k\left[ x,\,y,\,z \right]$. We give a new way to attack this question, based on the automata theory and the Newton polygon. This new approch allows us to generalize significantly the results of $\left[ \text{A} \right]$.

Keywords

14R10tame automorphismsautomataNewton polygon
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 55 , Issue 3 , 01 June 2003 , pp. 533 - 560
Copyright
Copyright © Canadian Mathematical Society 2003

References

Références

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