The dimension of the equisingular stratum of an isolated plane curve singularity

Abstract

Let C be an isolated plane curve singularity. Zariski defined and studied equisingular deformations of C, see [12], [13], [14], and proved that this is the same as \mu-constant deformations. Wahl [10] showed that the functor of equisingular deformations is smooth, say of dimension es(C). This therefore is also the dimension of the \mu-constant stratum. In this paper we give a formula for es(C).