On negative weight derivations of the moduli algebras of weighted homogeneous hypersurface singularities
type: Item
instance of: scholarly article
title: On negative weight derivations of the moduli algebras of weighted homogeneous hypersurface singularities
zbMATH Open document ID: 0836.32015
DOI: 10.1007/BF01460981
author: Hao Chen
published in: Mathematische Annalen
publication date: 1996-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/165359
review text: Let \((V,0) \subseteq (\mathbb{C}^{n + 1}, 0)\) be an isolated singularity defined by a quasihomogeneous polynomial \(f(x_0, x_1, \dots, x_n)\), \(A(V) = C\{x_0, x_1, \dots, x_n\} / (f, {\partial f \over \partial x_0}, {\partial f \over \partial x_1}, \dots, {\partial f \over \partial x_n})\) be its moduli algebra and \(L(V)\) be the Lie algebra of derivations on \(A(V)\). We prove that there is no negative weight derivation in \(L(V)\) in the case of \(n = 3\). Hence a microlocal characterization of quasihomogeneous singularities only using \(L(V)\) of Stephen S. T. Yau can be proved completely in the case of dimension 3.
Mathematics Subject Classification ID: 32S50
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 32S25
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 840176
zbMATH Keywords: isolated singularity
zbMATH Keywords: Lie algebra of derivations
reviewed by: Huayi Chen
MaRDI profile type: Publication
cites work: Nonexistence of negative weight derivation of moduli algebras of weighted homogeneous singularities
cites work: Classification of isolated hypersurface singularities by their moduli algebras
cites work: Quasihomogeneous isolated singularities of hyperplanes.
cites work: Solvable Lie algebras and generalized Cartan matrices arising from isolated singularities
description: scientific article; zbMATH DE number 840176