Relations between the leading terms of a polynomial automorphism

2008/08/13 by Philippe Bonnet, Bonnet, Philippe, Stéphane Vénéreau +1
Mathematics · #14R10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14R10

paper · pdf · doi:10.48550/arxiv.0808.1821

20 pages

arxiv created 2008/08/13 · arxiv updated 2009/12/01

Abstract

Let I be the ideal of relations between the leading terms of the polynomials defining an automorphism of Kⁿ. In this paper, we prove the existence of a locally nilpotent derivation which preserves I. Moreover, if I is principal, i.e. I=(R), we compute an upper bound for °₂(R) for some degree function °₂ defined by the automorphism. As applications, we determine all the principal ideals of relations for automorphisms of K³ and deduce two elementary proofs of the Jung-van der Kulk Theorem about the tameness of automorphisms of K².

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