Weakly quasihomogeneous hypersurface singularities in positive characteristic
type: Item
instance of: scholarly article
title: Weakly quasihomogeneous hypersurface singularities in positive characteristic
zbMATH Open document ID: 0759.14020
DOI: 10.1007/BF02571552
author: Safwan Aouira
author: Gerhard Pfister
published in: Mathematische Zeitschrift
publication date: 1992-09-26T00:00:00Z
full work available at URL: https://eudml.org/doc/174343
review text: \textit{K. Saito} in Invent. Math. 14, 123-142 (1971; Zbl 0224.32011) had given a characterisation of hypersurface singularities over the complex numbers admitting a good \(\mathbb{C}^*\)-action. This characterisation fails in positive characteristic. In the paper under review the authors prove a suitable version of this theorem in positive characteristic. They define a notion of weakly quasihomogeneous local rings and then they prove the following theorem: Let \(A=kx/(f)\) be the complete local ring of an isolated singularity and \({\mathfrak M}\) its maximal ideal. Then the following two conditions are equivalent: (1) \(A\) is weakly homogeneous. (2) There is a derivation \(\delta\in\text{Der}_ k{\mathfrak M}\) which is not nilpotent. The authors apply this theorem to the case of plane curves to derive various corollaries on the relations between the Milnor number, Tjurina number and other invariants of the plane curve.
reviewed by: N. Mohan Kumar
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14G15
zbMATH DE Number: 54907
zbMATH Keywords: hypersurface singularities
zbMATH Keywords: positive characteristic
zbMATH Keywords: weakly quasihomogeneous local rings
zbMATH Keywords: derivation
zbMATH Keywords: plane curves
zbMATH Keywords: Milnor number
zbMATH Keywords: Tjurina number
MaRDI profile type: Publication
cites work: Algebroid curves in positive characteristic
cites work: Numerische Charakterisierung Quasihomogener GORENSTEIN-Kurvensingularitäten
cites work: Quasihomogeneous isolated singularities of hyperplanes.
cites work: Über Derivationen in isolierten Singularitäten auf vollständigen Durchschnitten
OpenAlex ID: W1983744195
description: scientific article; zbMATH DE number 54907