Gusev, Gleb Monodromy zeta-functions of deformations and Newton diagrams. (English) Zbl 1174.14003 Rev. Mat. Complut. 22, No. 2, 447-454 (2009). 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. Reviewer: Gerhard Pfister (Kaiserslautern) Cited in 1 ReviewCited in 2 Documents MSC: 14B07 Deformations of singularities 32S30 Deformations of complex singularities; vanishing cycles 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.) 58K10 Monodromy on manifolds 58K60 Deformation of singularities Keywords:deformations of singularities; monodromy; zeta-function; Newton diagram PDFBibTeX XMLCite \textit{G. Gusev}, Rev. Mat. Complut. 22, No. 2, 447--454 (2009; Zbl 1174.14003) Full Text: DOI arXiv EuDML