On Schappert’s Characterization of Strictly Unimodal Plane Curve Singularities

Abstract

The representation theory of curve singularities (more precisely, of their local rings) has turned out to be closely related to their deformation properties. Namely, as was shown in [6],[9],[7], such a ring R is of finite type, that is has only finitely many torsion-free indecomposable modules (up to isomorphism), if and only if it dominates one of the so called simple plane curve singularities in the sense of [1]. In [4] the authors have shown that R is of tame type, that is it has essentially only 1-parameter families of indecomposable torsion-free modules, if and only if it dominates one of the unimodal plane curve singularities of type T pq (T pq2 in the classification of [1]).