Monodromy zeta-functions of deformations and Newton diagrams
type: Item
instance of: scholarly article
title: Monodromy zeta-functions of deformations and Newton diagrams
zbMATH Open document ID: 1174.14003
author: Gleb Gusev
published in: Revista Matemática Complutense
publication date: 2009-10-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1011.5383
full work available at URL: https://eudml.org/doc/43560
review text: 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.
reviewed by: Gerhard Pfister
Mathematics Subject Classification ID: 14B07
Mathematics Subject Classification ID: 32S30
Mathematics Subject Classification ID: 14D05
Mathematics Subject Classification ID: 58K10
Mathematics Subject Classification ID: 58K60
zbMATH DE Number: 5610832
zbMATH Keywords: deformations of singularities
zbMATH Keywords: monodromy
zbMATH Keywords: zeta-function
zbMATH Keywords: Newton diagram
MaRDI profile type: Publication
arXiv ID: 1011.5383
OpenAlex ID: W2055972380
DOI: 10.5209/REV_REMA.2009.V22.N2.16282
description: scientific article