A Simple Proof of Jung's Theorem on Polynomial Automorphisms of $\C^2$

Details A Simple Proof of Jung's Theorem on Polynomial Automorphisms of $\C^2$ A Simple Proof of Jung's Theorem on Polynomial Automorphisms of $\C^2$

2004-08-05

arxiv.org/abs/math/0408077v1

Acta Math. Vietnamica, N. 28 (2), 209-214, 2003

Mathematics

Algebraic Geometry

Scientific paper

The Automorphism Theorem, discovered first by Jung in 1942, asserts that if
$k$ is a field, then every polynomial automorphism of $k^2$ is a finite product
of linear automorphisms and automorphisms of the form $(x,y)\mapsto(x+p(y), y)
$ for $p\in k[y]$. We present here a simple proof for the case $k=\C$ by using
Newton-Puiseux expansions.

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