On simple \(\mathbb{Z}_2\)-invariant and corner function germs (Q2192164)

Let the cyclic group \(\mathbb Z_2=\langle \sigma \rangle\) of order \(2\) act on \((\mathbb C^{m+n},0)\) via \(\sigma(x_1,\ldots,x_m,y_1,\ldots,y_n)=(-x_1,\ldots,-x_m,y_1,\ldots,y_n)\). Let \(\mathbb Z_2^m=\langle \sigma_1,\ldots,\sigma_m\rangle\) act on \((\mathbb C^{m+n},0)\) via \[\sigma_i(x_1,\ldots,x_m,y_1,\ldots,y_n)=(x_1,\ldots,x_{i-1},-x_i,x_{i+1},\ldots,x_m,y_1,\ldots,y_n).\] Equivariantly simple function germs with respect to these actions (corner singularities) are classified up to stable equivalence. In both cases the property simple is characterized in terms of the intersection form respectively in terms of the monodromy.