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Artin Approximation Compatible with a Change of Variables

  Published:2016-07-11
 Printed: Dec 2016
  • Goulwen Fichou,
    IRMAR (UMR 6625), Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France
  • Ronan Quarez,
    IRMAR (UMR 6625), Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France
  • Masahiro Shiota,
    Graduate School of Mathematics, Nagoya University, Chikusa, Nagoya, 464-8602, Japan
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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 result is closely related to the so-called nested Artin approximation and becomes false in the analytic setting. We provide local and global versions of this approximation in real and complex geometry together with an application to the Right-Left equivalence of Nash maps.
Keywords: Artin approximation, global case, Nash functions Artin approximation, global case, Nash functions
MSC Classifications: 14P20, 58A07 show english descriptions Nash functions and manifolds [See also 32C07, 58A07]
Real-analytic and Nash manifolds [See also 14P20, 32C07]
14P20 - Nash functions and manifolds [See also 32C07, 58A07]
58A07 - Real-analytic and Nash manifolds [See also 14P20, 32C07]
 

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