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

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...

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Detalles Bibliográficos
Autores: Alberich-Carramiñana, María, Almirón, Patricio, Moyano-Fernández, Julio-José
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/7198
Acceso en línea:https://hdl.handle.net/20.500.14352/7198
Access Level:acceso abierto
Palabra clave:512.7
R-modules
Γ-semimodules
Curve singularities
Moduli
Value sets
Álgebra
Geometria algebraica
Grupos (Matemáticas)
1201 Álgebra
1201.01 Geometría Algebraica
Descripción
Sumario: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.