The deformations of the simple space curve singularities

Abstract

In [4] and [5] Marc Giusti classified the simple isolated complete intersection singularities of positive dimension. He showed that besides the simple hypersurface singularities there are only simple singularities of curves in complex 3-space. He gave a list of adjacencies between these singularities. Later V. V. Goryunov (see [6]) found some additional adjacencies, but the complete list remained unknown (see [1, p. 23]). In this note we prove the following theorem: Theorem The following diagram shows the complete list of adjacencies between the simple space curve singularities which are not hypersurface singularities. Here Giusti’s list is completed by the deformations Z10 → T9 and Z10 → U9. S5 S6 S7 S8 S9 · · ·