Nodal deformations of singularities (Q700047)

Deformations of a plane curve singularity \((X,0)\) to \(\delta(X,0)\) nodes are studied using the methods of A'Campo. In particular, it is proved that singularities of type \(y^{d-1} - x^d\), \(y^{2d-1} - x^{2d+1}\) can be deformed into real morsifications preserving the degree of the original polynomial. The results are partially covered by results of \textit{D. Pecker} [Ann. Inst. Fourier 49, 1439-1452 (1999; Zbl 0933.14013)], resp. \textit{E. Shustin} [Topology 32, 845-856 (1993; Zbl 0845.14017)].