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...
| Autores: | , , |
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| 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 |
| 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. |
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