New \(k\)-th Yau algebras of isolated hypersurface singularities and weak Torelli-type theorem
type: Item
instance of: scholarly article
title: New \(k\)-th Yau algebras of isolated hypersurface singularities and weak Torelli-type theorem
zbMATH Open document ID: 1499.14008
author: Naveed Hussain
author: Huaiqing Zuo
author: Stephen Yau
published in: Mathematical Research Letters
publication date: 2022-09-30T00:00:00Z
review text: Let \(V\) be a hypersurface with an isolated singularity at the origin and \(L(V)\) be the Yau algebra which is defined to be the Lie algebra of derivations of the moduli algebra. In the paper under review, the authors generalize the original Yau algebra \(L(V)\) to the \(k\)-th Yau algebra \(L^k(V)\). They obtain the weak Torelli-type theorems of simple elliptic singularities using Lie algebras \(L^1(V)\) and \(L^2(V)\). More precisely, they prove that \(L^2(\tilde{E}_6)\), \(L^1(\tilde{E}_7)\), \(L^2(\tilde{E}_7)\), \(L^1(\tilde{E}_8)\) and \(L^2(\tilde{E}_8)\) are non-trivial one-parameter families. Thus the weak Torelli-type theorems hold for simple elliptic singularities \(\tilde{E}_6\), \(\tilde{E}_7\) and \(\tilde{E}_8\). They also show that if \(X\) and \(Y\) are two simple hypersurface singularities, then \(L^1(X)=L^1(Y)\) as Lie algebras, if and only if \(X\) and \(Y\) are analytically isomorphic.
reviewed by: Rong Du
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 32S25
Mathematics Subject Classification ID: 17B66
zbMATH DE Number: 7595084
zbMATH Keywords: Yau algebras
zbMATH Keywords: isolated hypersurface singularity
zbMATH Keywords: weak Torelli-type theorem
MaRDI profile type: Publication
DOI: 10.4310/MRL.2022.V29.N2.A7
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description: scientific article; zbMATH DE number 7595084