A Simple Proof of Jung's Theorem on Polynomial Automorphisms of \C²

2004/08/05 by Nguyen Van Chau
Mathematics · #math.AG #math.AC #msc:14R

paper · pdf

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

arxiv created 2004/08/05 · arxiv updated 2009/12/01

Abstract

The Automorphism Theorem, discovered first by Jung in 1942, asserts that if k is a field, then every polynomial automorphism of k² is a finite product of linear automorphisms and automorphisms of the form (x,y)↦(x+p(y), y) for p∈ k[y]. We present here a simple proof for the case k=\C by using Newton-Puiseux expansions.

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