7 citations · 15 across the 15 of their papers we have counts for
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Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent
Guillaume Rond
We answer in the negative the long-standing open question of whether biholomorphic equivalence implies algebraic equivalence for germs of real algebraic manifolds in .…
A proof of A. Gabrielov's rank Theorem
André Belotto da Silva, Octave Curmi, Guillaume Rond
This article contains a complete proof of Gabrielov's rank Theorem, a fundamental result in the study of analytic map germs. Inspired by the works of Gabrielov and Tougeron, we dev…
Transcendental holomorphic maps between real algebraic manifolds in a complex space
Guillaume Rond
We give an example of a real algebraic manifold embedded in a complex space that does not satisfy the Nash-Artin approximation Property. This Nash-Artin approximation Property is c…
An irreducibility criterion for power series
Guillaume Rond, Bernd Schober
We prove an irreducibility criterion for polynomials with power series coefficients generalizing previous known results concerning quasi-ordinary polynomials.
Higher order approximation of analytic sets by topologically equivalent algebraic sets
Marcin Bilski, Krzysztof Kurdyka, Adam Parusinski +1
It is known that every germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that the homeomorphism can be chosen in such a way that the an…