Representation theory for log-canonical surface singularities

Gustavsen, Trond Stølen; Ile, Runar

Annales de l'Institut Fourier, Tome 60 (2010) no. 2, pp. 389-416.

Nous considérons la théorie des représentations pour une classe des singularités des surfaces log-canoniques dans le sens de modules réflexifs (ou d’une manière équivalente, modules maximals de Cohen-Macaulay) et dans le sens de représentations de dimension finie du groupe fondamental local. Une classification et une énumération détaillées des modules réflexifs indécomposables sont données, et nous montrons que n’importe quel module réflexif admet une connexion intégrable, et par conséquent est induit par une représentation de dimension finie du groupe fondamental local.

We consider the representation theory for a class of log-canonical surface singularities in the sense of reflexive (or equivalently maximal Cohen-Macaulay) modules and in the sense of finite dimensional representations of the local fundamental group. A detailed classification and enumeration of the indecomposable reflexive modules is given, and we prove that any reflexive module admits an integrable connection and hence is induced from a finite dimensional representation of the local fundamental group.

Classification : 13C14, 32S40, 14J17
Keywords: Surface singularity, maximal Cohen-Macaulay module, integrable connection, elliptic curve, local fundamental group
Mot clés : singularité d’une surface, module maximal de Cohen-Macaulay, connexion intégrable, courbe elliptique, groupe fondamental local

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