\Sigma$ over a base $S$ consist a flat deformation of $\Xi {\longrightarrow}S$ of $\Sigma$, together with a deformation of the $F:({{\mathbb C}}^n \times S,0){\longrightarrow}({{\mathbb C}}\times S,0)$, such that $\Xi$ is contained in the critical locus of $F$. We refer to [@pellikaan2] and [@dJvS1] for more details. There is a notion of good represenetatives for the germs involved and such a good representative of a one-parameter deformation $F$, $\Xi$ is called a [*morsification*]{}, if for $t \neq 0$ the curve $\Xi_t$ is smooth and the critical points of $F_t: X {\longrightarrow}{{\mathbb C}}$ are of the simplest possible type, namely $A_1$, $A_{\infty}$ or $D_{\infty}$. If the curve $\Sigma$ defined by $I$ is smoothable, and $f \in I^2$, then morsifications do exist ([@pellikaan2], prop. 3.4). But even for functions of three variables morsifications do not alway exist, as triple points $f=xyz$ generically occur. Allowing for these leads to the notion of [*disentanglement*]{}, but even these do not always exists, as projections of non-smoothable normal surfaces singularities to $({{\mathbb C}}^3,0)$ show. The following result can be found in [@pellikaan2].

(Pellikaan, [@pellikaan2], prop. 2.19) If $f$ posesses a morsification, then $$\dim(I/J_f)=\# A_1 +\# D_{\infty}$$

where $\# A_1$ and $\# D_{\infty}$ denote the number of these 