Normal subgroup generated by a plane polynomial automorphism

Abstract

We study the normal subgroup <f> generated by a non trivial element f in the group G of complex plane polynomial automorphisms having Jacobian determinant 1. On one hand if f has length at most 8 relatively to the classical amalgamated product structure of G, we prove that <f> = G. On the other hand if f is a sufficiently generic element of even length at least 14, we prove that <f> is a proper subgroup of G.

Some minor corrections

References in corpus (1)

• Transformations birationnelles de petit degré

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