Equisingular algebraic approximation of real and complex analytic germs

2019/10/25 by Adamus, Janusz, Patel, Aftab
#13C14 #13H10 #14P15 #14P20 #32B99 #32C07 #32S05 #32S10 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.11498

Abstract

We show that a Cohen-Macaulay analytic singularity can be arbitrarily closely approximated by germs of Nash sets which are also Cohen-Macaulay and share the same Hilbert-Samuel function. We also prove that every analytic singularity is topologically equivalent to a Nash singularity with the same Hilbert-Samuel function.

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