On the Nash points of subanalytic sets
André Belotto da Silva, Octave Curmi, and Guillaume Rond
Journal of Singularities
volume 27 (2024), 68-88
Received: 18 September 2023. In revised form: 28 March 2024
Abstract:
Based on a recently developed rank theorem for Eisenstein power series, we provide new proofs of the following two results of W. Pawłucki:
I) The non-regular locus of a complex or real analytic map is an analytic set.
II) The set of semianalytic or Nash points of a subanalytic set X is a subanalytic set, whose complement has codimension two in X.
2010 Mathematical Subject Classification:
Primary 13B10, 14P20, 32C07; Secondary 13A18, 13J05, 32B20
Key words and phrases:
Subanalytic set, Nash set, regular map
Author(s) information:
André Belotto da Silva
Université Paris Cité and Sorbonne Université
CNRS, IMJ-PRG
F-75013 Paris, France
email: andre.belotto@imj-prg.fr
Octave Curmi
Alfréd Rényi Institute of Mathematics
Budapest, Hungary
email: octave.curmi@proton.me
Guillaume Rond
Université Aix-Marseille
Institut de Mathématiques de Marseille (UMR CNRS 7373)
Centre de Mathématiques et Informatique
39 rue F. Joliot Curie
13013 Marseille, France
email: guillaume.rond@univ-amu.fr