Browsing by Author "Maubach, Stephan"
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- ItemA characterization of semisimple plane polynomial automorphisms(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2008) Maubach, Stephan; Furter, Jean-PhilippeIt is well-known that an element of the linear group GLn(C) is semisimple if and only if its conjugacy class is Zariski closed. The aim of this paper is to show that the same result holds for the group of complex plane polynomial automorphisms.
- ItemThe Nagata automorphism is shifted linearizable(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2008) Maubach, Stephan; Poloni, Pierre-MarieA polynomial automorphism F is called shifted linearizable if there exists a linear map L such that LF is linearizable. We prove that the Nagata automorphism N:=(X−YΔ−ZΔ2,Y+ZΔ,Z) where Δ=XZ+Y2 is shifted linearizable. More precisely, defining L(a,b,c) as the diagonal linear map having a,b,c on its diagonal, we prove that if ac=b2, then L(a,b,c)N is linearizable if and only if bc≠1. We do this as part of a significantly larger theory: for example, any exponent of a homogeneous locally finite derivation is shifted linearizable. We pose the conjecture that the group generated by the linearizable automorphisms may generate the group of automorphisms, and explain why this is a natural question.