Representation theory for log-canonical surface singularities
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.
scientific article; zbMATH DE number 5726198
scientific article