On adjacencies of singularities \(A_ k\) to points of the \(\mu =const\) stratum of a singularity
type: Item
instance of: scholarly article
title: On adjacencies of singularities \(A_ k\) to points of the \(\mu =const\) stratum of a singularity
zbMATH Open document ID: 0555.32008
DOI: 10.1007/BF01076726
author: Sabir M. Gusein-Zade
author: N. N. Nekhoroshev
publication date: 1983-01-01T00:00:00Z
review text: It is shown first that if an \(A_ k\)-singularity is adjacent to a singularity corresponding to a general (or, equivalently, to any) point on the \(\mu =const\quad stratum\) of the singularity \(f_ m=x^ m+y^ m,\) then \(k\leq k(m):=(m^ 2+m-6)/2\). Next, for \(m=22\) and for a special (explicit) singularity X on the \(\mu =const\quad stratum\) of \(f_{22}\) it is shown that \(A_{257}\) is adjacent to X. Since \(k(22)=250\), it follows that the highest adjacent \(A_ k\)-singularity is not the same along the \(\mu =const\) stratum of \(f_{22}\).
reviewed by: Alexandru Dimca
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
Mathematics Subject Classification ID: 32S60
zbMATH DE Number: 3884474
zbMATH Keywords: constant Milnor number
zbMATH Keywords: stratification
zbMATH Keywords: \(A_ k\)-singularity
MaRDI profile type: Publication
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3884474