Artin approximation compatible with a change of variables
Algebraic Geometry
2019-08-15 v1
Abstract
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.
Cite
@article{arxiv.1511.01262,
title = {Artin approximation compatible with a change of variables},
author = {Goulwen Fichou and Ronan Quarez and Masahiro Shiota},
journal= {arXiv preprint arXiv:1511.01262},
year = {2019}
}