The structure of the discriminant of some space-curve singularities

Among the space-curve singularities of the simplest type are the so called wedges D = C boolean OR L, consisting of a plane-curve singularity C togeth er with a line L transverse to the plane of C. In this note we describe the discriminant of D in terms of C. In particular, we show that the complemen t of the discriminant of D is a K(pi, 1) if the complement of the discrimin ant of C is a K(pi, 1). We also give a formula for the multiplicity of the discriminant of C boolean OR L.