A hyperplane section theorem for Milnor numbers
type: Item
instance of: scholarly article
title: A hyperplane section theorem for Milnor numbers
zbMATH Open document ID: 0887.14003
published in: Mathematische Annalen
publication date: 1998-05-25T00:00:00Z
review text: We prove the following result. Theorem. Let \(R\) denote the power series ring \(\mathbb{C} X_1,X_2, \dots, X_n\) and \(f\in R\) any irreducible element. Assume that for any element \(h\in R\) which is a part of a minimal system of generators of the maximal ideal of \(R\) the ring \(R/(f,h)\) has an isolated singular point. Then the set of Milnor numbers of the rings \(R/(f,h)\) with any \(h\) as above is bounded above. The converse of this result is also true and it was observed by A. J. Parameswaran.
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 13F25
Mathematics Subject Classification ID: 32S05
zbMATH DE Number: 1121710
zbMATH Keywords: intersection multiplicity of plane curves
zbMATH Keywords: power series ring
zbMATH Keywords: isolated singular point
zbMATH Keywords: Milnor numbers
author: Rajendra Gurjar
MaRDI profile type: Publication
full work available at URL: s002080050116
OpenAlex ID: W2036915167
DOI: 10.1007/S002080050116
Recommended article: On the Milnor number of a generic hyperplane section
Recommended article: Milnor numbers and the topology of polynomial hypersurfaces
Recommended article: A generalization of a theorem of Milnor
Recommended article: Hyperplane Arrangements and Mixed Hodge Numbers of the Milnor Fiber
Recommended article: Hyperplane arrangements and Milnor fibrations
Recommended article: Q3744274
Recommended article: Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs
Recommended article: The Lefschetz Theorem for Hyperplane Sections
Recommended article: Milnor numbers and Euler obstruction
Recommended article: A generalization of the Lefschetz hyperplane-section theorem
description: scientific article; zbMATH DE number 1121710