On the closure of the tame automorphism group of affine three-space

Eric Edo (1) , Pierre-Marie Poloni (2)

1 ERIM - Equipe de Recherche en Informatique et Mathématiques
2 Unibas - Université de Bâle = University of Basel = Basel Universität

We provide explicit families of tame automorphisms of the complex affine three-space which degenerate to wild automorphisms. This shows that the tame subgroup of the group of polynomial automorphisms of $\C^3$ is not closed, when the latter is seen as an infinite dimensional algebraic group.tomorphism group of affine three-space

Mots clés: polynomial automorphisms; tame and wild automorphisms; ind-varieties

Domaines: Géométrie algébrique [math.AG]

Eric Edo, Pierre-Marie Poloni. On the closure of the tame automorphism group of affine three-space. 2014. ⟨hal-00958234v2⟩