Monodromy zeta-functions of deformations and Newton diagrams
Let \(F:(\mathbb{C}^{n+1}, 0)\to (\mathbb{C}, 0)\) be the germ of an analytic function. Assume that the Newton diagram \(\Gamma\) of \(F\) is non-degenerate. Consider \(f_t=F(t, z_1, \dots, z_n)\) as \(1\)-parameter-deformation of the germ defined by \(f_0:=F(0,z_1, \dots, z_n)\). A formulae for the monodromy zeta-functions of the deformations of the hypersurface germs \(\{f_0=0\}\cap(\mathbb{C}^\ast)^n\) and \(\{f_0=0\}\) at the origin in terms of the Newton diagram \(\Gamma\) is given.
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