\[
  C \overset{\approx}{\underset{\approx}{\rightleftarrows}} C' .
\]

\[
  \bigl(\, \text{\struck{$B \times I \hookrightarrow$}}\; B \subset C \subset X,
  \quad C \text{ vois. de } B,\quad \exists\, C \xrightarrow[\sim]{\varphi} B \times I,
\]

\[
  \text{et } \dot C = \varphi^{-1}(B \times \{1\}) \,\bigr)
\]

\[
  (C, \dot C) \xrightarrow[\sim]{\rho} \mathrm{Cone}(\text{\struck{$\dot Y$}}\, Y) \qquad (\text{avec } \rho(a) = o).
\]

\[
  V - Y = V^* \simeq \dot V \times [0, 1[ ,
\]

\[
  X \simeq \bigl( (X \smallsetminus (\dot V \smallsetminus V)) \amalg (\dot V \times I) \bigr) \textstyle\coprod_{\dot V \times \{1\}} Y ,
\]

\[
  (X', B, Y, \varphi) \longmapsto \bigl( (X' \textstyle\coprod_B (Y, \varphi)),\, Y \bigr)
\]

\[
  \Big\downarrow \approx
\]

\[
  (X, Y) \text{ paires équisingulières.}
\]

\[
  \varepsilon \wedge \varepsilon^* \wedge \omega(Q) = 1, \qquad \omega(Q) \simeq \omega(Q^*), \qquad
  Q^* \simeq \varepsilon \wedge Q,\quad Q \simeq \varepsilon^* \wedge Q^*
\]

\[
  \mathfrak{S}_{P(V)} \simeq \mathrm{Aut}(V)(\mathbb{F}_3) \simeq \mathrm{GP}(1, \mathbb{F}_3)
\]

\[
  \omega(Q) \simeq \omega(Q^*) = \omega, \qquad \text{\struck{\ill{}}}\; \boxed{\varepsilon^* \wedge \varepsilon \wedge \omega = 1}
\]

\[
  \boxed{Q^* = \varepsilon \wedge Q^\vee,\quad Q \simeq \varepsilon \wedge Q^*}
\]

\[
  \varepsilon \wedge \mathrm{codiag}\, Q \simeq \varepsilon^* \wedge \mathrm{codiag}\, Q^*
  \qquad (\text{au-dessus : } \omega(S_6),\ \omega(S_6^*))
\]

\[
  \{a, b\} \wedge \{u, u'\} \to \{v, v'\}
\]

\[
  \text{\struck{$\{a, b\} \wedge$}} \qquad a \wedge u = v, \qquad a \wedge v = u'
\]

\[
  \{a, b\} \wedge \{u, u'\} \wedge \{v, v'\} \simeq \text{\struck{\ill{}}}\; \mathrm{diag}\, Q,
  \qquad \{u, u'\} \wedge \{v, v'\} = \mathrm{codiag}(Q),
  \qquad \{a, b\} \simeq \omega(Q)
\]

\[
  \simeq \text{\struck{\ill{}}}\; \omega(S \amalg \varepsilon) \simeq \omega(S) \wedge \varepsilon
  \simeq \mathrm{codiag}(Q) \wedge \varepsilon \simeq \mathrm{diag}\, Q \quad \text{OK !}
\]

\[
  \begin{array}{lcl}
    \text{\struck{$a$}}\,bc \ (\text{entouré}) & & ac \\
    bcu & & bc \\
    ac\,u \ (\text{entouré}) & & ab \\
    \text{délicat}\ abc' & & c'a \\
    \text{\struck{$c'ab$}} \text{ ou } c'ab' & & c'b' \\
    \text{\struck{$c'b$}}u \text{ ou } c'bu' & &
  \end{array}
\]

\[
  \begin{cases}
    \mathrm{card}\, E = 12 \\
    \forall\, a, b \in E, \text{ on a } \mathrm{card}\, a \cap b \leqslant 1
  \end{cases}
\]

\[
    1 \to \mathfrak{S}_3 \times \mathfrak{S}_3 \to \mathrm{Aut} \text{ d'une bi-ditriade} \to \text{\struck{\ill{}}}\; 1
  \]

\[
    1 \to (\mathfrak{S}_3 \times \mathfrak{S}_3)' \to \mathrm{Aut} \text{ d'une quadritriade} \to \mathfrak{S}_4 \to 1,
  \]

\[
    (\mathfrak{S}_3 \times \mathfrak{S}_3)' = \{(u, v) \mid \varepsilon(u) = \varepsilon(v)\},
    \qquad \mathrm{Aut} \text{ d'une quadritriade} \simeq \mathrm{Aff}(2, \mathbb{F}_3)
  \]