7 citations · 15 across the 15 of their papers we have counts for
6 papers · 1 filter
On the Nash points of subanalytic sets
Andre Belotto da Silva, Octave Curmi, Guillaume Rond
Based on a recently developed rank Theorem for Eisenstein power series, we provide new proofs of the following two results of W. Pawlucki: I) The non regular locus of a complex or…
On rank Theorems for morphisms of local rings
André Belotto da Silva, Octave Curmi, Guillaume Rond
We prove a generalization of Gabrielov's rank theorem for families of rings of power series which we call W-temperate. Examples include the families of complex analytic functions a…
Algebraic varieties are homeomorphic to varieties defined over number fields
Adam Parusinski, Guillaume Rond
We show that every affine or projective algebraic variety defined over the field of real or complex numbers is homeomorphic to a variety defined over the field of algebraic numbers…
Remark on a theorem of H. Hauser on textile maps
Guillaume Rond
We give a counter example to the new theorem that appeared in the survey \cite{H} on Artin approximation. We then provide a correct statement and a proof of it.
Local topological algebraicity with algebraic coefficients of analytic sets or functions
Guillaume Rond
We prove that any complex or real analytic set or function germ is topologically equivalent to a germ defined by polynomial equations whose coefficients are algebraic numbers.
Local topological algebraicity of analytic function germs
Marcin Bilski, Adam Parusinski, Guillaume Rond
T. Mostowski showed that every (real or complex) germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that every (real or complex) analyti…