3 papers
math.AG2025
Płoski Approximation Theorem
Adam Parusiński, Guillaume Rond
The aim of this paper is to review how some approximation results in commutative algebra are being used to construct equisingular deformations of singularities. The first example o…
math.NT2024
About Eisenstein's Theorem
Guillaume Rond
The aim of this survey papier is to present a result due to Eisenstein, to prove a generalized version of it, and to present some applications of this Eisenstein's Theorem, in part…
math.AC2014
The analogue of Izumi's Theorem for Abhyankar valuations
Guillaume Rond, Mark Spivakovsky
A well known theorem of Shuzo Izumi, strengthened by David Rees, asserts that all the divisorial valuations centered in an analytically irreducible local noetherian ring are linear…