Ploski Approximation Theorem

2025/05/18 by Parusiński, Adam, Rond, Guillaume
#14B05. 32S05 #14B12 #32B10 #32S15 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.12356

Abstract

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 of such an approximation result appeared for the first time in A. Ploski's PhD thesis.

Citations

• On the algebraicity of germs of meromorphic functions
• Zariski's dimensionality type of singularities. case of dimensionality type 2
• Algebro-geometric equisingularity of Zariski
• Higher order approximation of analytic sets by topologically equivalent algebraic sets
• Formal and convergent solutions of analytic equations
• Arcwise Analytic Stratification, Whitney Fibering Conjecture and Zariski Equisingularity
• Local topological algebraicity of analytic function germs

Related

• A remark on equisingular approximations of quasi-plurisubharmonic functions
• On equisingular approximation of plurisubharmonic functions
• Algorithmic equiresolution of deformations of embedded varieties
• A survey on algebraic dilatations
• Equisingular calculations for plane curve singularities