Artin approximation compatible with a change of variables

Goulwen Fichou (1) , Ronan Quarez (1) , Masahiro Shiota (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Graduate School of Mathematics [Nagoya]

We propose a version of the classical Artin approximation which allows to perturb the variables of the approximated solution. Namely, it is possible to approximate a formal solution of a Nash equation by a Nash solution in a compatible way with a given Nash change of variables. This results is closely related to the so-called nested Artin approximation and becomes false in the analytic setting. We provide local and global version of this approximation in real and complex geometry together with an application to the Right-Left equivalence of Nash maps.

Mots clés: Artin approximation; global case; Nash functions

Domaines: Géométrie algébrique [math.AG]

Goulwen Fichou, Ronan Quarez, Masahiro Shiota. Artin approximation compatible with a change of variables. Canadian Mathematical Bulletin, 2016, 59 (4), pp.760-768. ⟨10.4153/CMB-2016-034-1⟩. ⟨hal-01224084⟩