A classification of weighted homogeneous Saito free divisors
type: Item
instance of: scholarly article
title: A classification of weighted homogeneous Saito free divisors
zbMATH Open document ID: 1189.32017
author: Jiro Sekiguchi
published in: Journal of the Mathematical Society of Japan
publication date: 2009-12-22T00:00:00Z
full work available at URL: article
review text: The purpose of the paper is to obtain a complete list of weighted homogeneous Saito free divisors in the three-dimensional affine space over \(\mathbb C\). The approach is mainly based on properties of Lie algebras of vector fields tangent to reduced hypersurfaces at their non-singular points. A complete list of such Lie algebras consists of 17 weighted homogeneous polynomials. This set is naturally subdivided in three subsets containing 2, 7 and 8 elements related with discriminants of irreducible real reflection groups of type \(A_3,\) \(B_3\) and \(H_3,\) respectively. Then, some interesting relationships between 17 polynomials and root systems of types \(E_{6}, E_{7}\) and \(E_{8}\) as well as few examples in higher dimensional cases are briefly discussed. In fact, the computational part of the work is a strong simplification of earlier results from [in: Algebraic analysis and number theory, RIMS Kôkyûroku 810, 85--94 (1992; Zbl 0966.17500)].
reviewed by: Aleksandr G. Aleksandrov
Mathematics Subject Classification ID: 32S25
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 32S65
zbMATH DE Number: 5651144
zbMATH Keywords: logarithmic vector fields
zbMATH Keywords: discriminants
zbMATH Keywords: Saito free singularities
zbMATH Keywords: Coxeter groups
zbMATH Keywords: Lie algebras
zbMATH Keywords: deformations
MaRDI profile type: Publication
OpenAlex ID: W2039724502
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DOI: 10.2969/JMSJ/06141071
description: scientific article; zbMATH DE number 5651144