in the germ of $\Gamma_P$ at ${{\mathbb P}}^n \times \{ 0\}\times {{\mathbb P}}$, respectively in the germ of $\Delta_P$ at $\{ 0\}\times {{\mathbb P}}$, we shall tacitly use the same notations for the germs.

It follows from the definition that $\Gamma_P$ is a closed analytic set and its affine part $\Gamma_P  \cap 
({{\mathbb C}}^n\times {{\mathbb C}}^k \times {{\mathbb C}})$ is just the union, over $s\in {{\mathbb C}}^k$, of the affine critical loci of the polynomials $f_s$. Note that, if $\dim {{\rm{Sing\hspace{2pt}}}}f_s \le 0$ for any $s$, then $\dim \Gamma_P \le k$.

Affine critical locus of [[$\mathcal F$[[ISI]{}]{}]{}]{} deformations
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Let now assume that $P$ is a one-parameter [[$\mathcal F$[[ISI]{}]{}]{}]{}  deformation. It follows that, if $\Gamma_P$ is not empty, then it is a curve.

An irreducible component $\Gamma_i$ of the germ $\Gamma_P$ can be of one of the following three types:

-   Type I: $\Gamma_i \cap \{\sigma =0\} \in {{\mathbb C}}^n \times \{ 0\} \times  {{\mathbb C}}$. Then $\Gamma_i$ is not in the neighbourhood of infinity.

-   Type II: $\Gamma_i \cap \{\sigma =0\} \in {{\mathbb Y}}^{{\infty}}$, a point having finite $t$-coordinate.

-   Type III: $\Gamma_i \cap \{\sigma =0\}$ is a point having infinite $t$-coordinate.

Let us decompose $\Gamma_P = \Gamma_I \cup 