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]).
Supported by DFG and International Science Foundation, grant RKJ000.
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Dedicated to Egbert Brieskorn on the occasion of his 60th birthday
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Drozd, Y.A., Greuel, GM. (1998). On Schappert’s Characterization of Strictly Unimodal Plane Curve Singularities. In: Arnold, V.I., Greuel, GM., Steenbrink, J.H.M. (eds) Singularities. Progress in Mathematics, vol 162. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8770-0_1
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