Curve singularities with one Puiseux pair and value sets of modules over their local rings

Abstract

In this paper we characterize the value set ∆ of the R-modules of the form R+zR for the local ring R associated to a germ ξ of an irreducible plane curve singularity with one Puiseux pair. In the particular case of the module of Kähler differentials attached to ξ , we recover some results of Delorme. From our characterization of ∆ we introduce a proper subset of semimodules over the value semigroup of the ring R. Moreover, we provide a geometric algorithm to construct all possible semimodules in this subset for a given value semigroup.