On adjacencies of singularities \(A_ k\) to points of the \(\mu =const\) stratum of a singularity
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 \(f_{22}\).
scientific article; zbMATH DE number 3884474