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

Publication

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

Journal Article (2025)

Journal

Journal of Algebraic Combinatorics

Pages

1-20

Volume

Number

Doc link

https://doi.org/10.1007/s10801-025-01382-x

File

Download the digital copy of the doc pdf document

Authors

Alberich Carramiñana, Maria
Almirón, Patricio
Moyano-Fernández, Julio-José

Abstract

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

Author keywords

R-modules, semimodules, curve singularities, moduli, value sets

Scientific reference

M. Alberich-Carramiñana, P. Almirón and J. Moyano-Fernández. Curve singularities with one Puiseux pair and value sets of modules over their local rings. Journal of Algebraic Combinatorics, 61(20): 1-20, 2025, to appear.