Representation theory for log-canonical surface singularities
type: Item
instance of: scholarly article
title: Representation theory for log-canonical surface singularities
zbMATH Open document ID: 1203.13012
author: Trond Stølen Gustavsen
author: Runar Ile
publication date: 2010-06-25T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/116275
review text: It is known that a normal surface singularity \((X,x)\) is \textit{log-canonical} if and only if the local fundamental group \(\pi_1^{\text{loc}}(X,x)\) is finite or solvable. The class of log-canonical surface singularities constitues exactly of the quotient singularities, the simple elliptic singularities, the cusp singularities, and finite quotients of these. In the paper under review the authors consider quotients of simple elliptic surface singularities and study the representation theory for this class of singularities. They obtain results both in terms of reflexive (or equivalently maximal Cohen-Macaulay) modules and in terms of finite dimensional representations of the local fundamental group \(\pi_1^{\text{loc}}(X,x)\), giving a detailed classification and enumeration of the indecomposable reflexive modules. One of the main result is that any reflexive module admits an integrable connection and therefore it is induced from a finite representation of the local fundamental group.
reviewed by: Cornel Baetica
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 32S40
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 32S25
zbMATH DE Number: 5726198
zbMATH Keywords: Surface singularity
zbMATH Keywords: maximal Cohen-Macaulay module
zbMATH Keywords: integrable connection
zbMATH Keywords: elliptic curve
zbMATH Keywords: local fundamental group
MaRDI profile type: Publication
OpenAlex ID: W2313092189
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DOI: 10.5802/AIF.2526
published in: Annales de l’institut Fourier
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description: scientific article; zbMATH DE number 5726198