Equisingular algebraic approximation of real and complex analytic germs

Janusz Adamus and Aftab Patel

Journal of Singularities
volume 20 (2020), 289-310

Received: 13 August 2020. Received in revised form: 7 October 2020

DOI: 10.5427/jsing.2020.20n

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Abstract:

We show that a Cohen-Macaulay analytic singularity can be arbitrarily closely approximated by Nash germs 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.


2010 Mathematical Subject Classification:

32S05, 32S10, 32B99, 32C07, 14P15, 14P20, 13H10, 13C14


Author(s) information:

Janusz Adamus Aftab Patel
Department of Mathematics Department of Mathematics
The University of Western Ontario The University of Western Ontario
London, Ontario, Canada N6A 5B7 London, Ontario, Canada N6A 5B7
email: jadamus@uwo.ca email: apate378@uwo.ca
and
Institute of Mathematics
Polish Academy of Sciences
ul. śniadeckich 8
00-656 Warsaw, Poland