\Gamma_{II} \cup \Gamma_{III}$ according to these types. If the total Milnor number $\mu(s)$ is not constant in the deformation $P$, then necessarily $\Gamma_{II} \cup \Gamma_{III} \not= \emptyset$. The points where $\Gamma_{II}$ intersects the hyperplane at infinity are shown to play an important role. The similar question for $\Gamma_{III}$ requires the completion with $t={{\infty}}$.

\[l:curve2\] Let $P$ be a one-parameter [[$\mathcal F$[[ISI]{}]{}]{}]{}  deformation. Then $\Gamma_{II}\cap  \{ x_0= 0 \}\subset 
\Sigma_0 \times \{ 0\} \times{{\mathbb C}}$ and $\Gamma_{III}\cap  \{ x_0= 0 \}\subset W_0\times \{ 0\} \times \{ {{\infty}}\}$.

From the definition of $\Gamma_P$ it follows that $\Gamma_P \cap \{ \sigma =s\} \subset 
{{\mathbb C}}^n \times {{\mathbb C}}$, for any $s\not= 0$. Therefore $\Gamma_P \cap \{ x_0= 0 \}\subset H^{{\infty}}\times \{ 0\} \times {{\mathbb C}}$. The curve $\Gamma_P \cap {{\mathbb Y}}$ is included into the critical set of the map $\bar \Psi = 
(\sigma, \tau) : {{\mathbb Y}}\to {{\mathbb C}}\times {{\mathbb P}}$. Slicing this with $\{ x_0= 0 \}$ and $\{ \sigma =0\}$ gives $\{ \frac{\partial 
P_d}{\partial x} (x,0) = 0, \ P_{d-1}(x,0) = 0\} \times {{\mathbb C}}$.

For $\Gamma_{III}$, we homogenise the equations of $\Gamma_P \cap ({{\mathbb C}}^n \times {{\mathbb C}}\times 
{{\mathbb C}})$, which are $\{ \frac{\partial P}{\partial x} (x,s) = 0, 