Generic linear sections of complex hypersurfaces and monomial ideals
type: Item
instance of: scholarly article
title: Generic linear sections of complex hypersurfaces and monomial ideals
zbMATH Open document ID: 1238.32019
author: Carles Bivià-Ausina
published in: Topology and its Applications
publication date: 2012-03-02T00:00:00Z
review text: Let \(f:(\mathbb{C}^{n},0)\rightarrow (\mathbb{C},0)\) be an analytic function germ with an isolated singularity at the origin. Let \(\mu ^{\ast }(f)=\big(\mu ^{(n)}(f),\dots ,\mu ^{(i)}(f),\dots ,\mu ^{\left( 0\right) }(f)\big)\) be the sequence of Milnor numbers of the restriction of \(f\) to a generic plane in \( \mathbb{C}^{n}\) of dimension \(i.\) So, \(\mu ^{(n)}(f)=\mu (f)\) is the standard Milnor number of \(f,\) \(\mu ^{(1)}(f)=\text{ord}f-1\) and \(\mu ^{(0)}(f)=1.\) The author gives an expression for the sequence \(\mu ^{\ast }(f)\) in terms of the Newton polyhedron of \(f\) under the condition that \(f\) is non-degenerate (the famous Kouchnirenko formula gives an expression for \( \mu ^{(n)}(f)\) only).
reviewed by: Tadeusz Krasiński
Mathematics Subject Classification ID: 32S05
zbMATH DE Number: 6011292
zbMATH Keywords: singularity
zbMATH Keywords: Milnor number
zbMATH Keywords: Whitney condition
zbMATH Keywords: Newton polyhedra
describes a project that uses: SINGULAR
MaRDI profile type: Publication
full work available at URL: j.topol.2011.09.015
OpenAlex ID: W2066583795
cites work: Milnor Number of Weighted-Le-Yomdin Singularities
cites work: Separating sets, metric tangent cone and applications for complex algebraic germs
cites work: Mixed Newton numbers and isolated complete intersection singularities
cites work: Joint reductions of monomial ideals and multiplicity of complex analytic maps
cites work: Q4097535
cites work: Les conditions de Whitney impliquent `\(\mu(*)\) constant'
cites work: Q3407115
cites work: Lokale topologische Eigenschaften komplexer Räume
cites work: Q3414477
cites work: Polyedres de Newton et nombres de Milnor
cites work: Calculation of Milnor number of isolated singularity of complete intersection
cites work: Variétés polaires locales et classes de Chern des variétés singulieres
cites work: Q4001976
cites work: On the Milnor number of a generic hyperplane section
cites work: Q3491907
cites work: Generalizations of Reductions and Mixed Multiplicities
cites work: Q4870611
cites work: Mixed Multiplicities, Joint Reductions and Quasi-Unmixed Local Rings
cites work: Q4047653
cites work: Q4083551
cites work: Q5465151
cites work: Variétés polaires. I: Invariants polaires des singularites d'hypersurfaces
cites work: Topologically Principal Part of Analytic Functions
DOI: 10.1016/J.TOPOL.2011.09.015
Recommended article: Q4202167
Recommended article: MULTIPLICITY AND ŁOJASIEWICZ EXPONENT OF GENERIC LINEAR SECTIONS OF MONOMIAL IDEALS
Recommended article: Linear Sections of Determinantal Varieties
Recommended article: Generic hyperplane section of curves and an application to regularity bounds in positive characteristic
Recommended article: On the generic hyperplane section of curves in positive characteristic
Recommended article: Q3367311
Recommended article: Monomial curves and schemes supported on lines
Recommended article: Multiplier ideals of monomial space curves
Recommended article: Linear systems of hyperplane sections on varieties of low codimension
Recommended article: Q3481861
description: scientific article; zbMATH DE number 6011292