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

被引:0
|
作者
Alberich-Carraminana, Maria [1 ,2 ]
Almiron, Patricio [3 ]
Moyano-Fernandez, Julio-Jose [4 ,5 ]
机构
[1] BarcelonaTech, Dept Matemat, Ave Diagonal 647, Barcelona 08028, Spain
[2] UPC, BarcelonaTech, Inst Matemat UPC BarcelonaTech IMTech, Inst Robot & Informat Ind IRI,CSIC, Ave Diagonal 647, Barcelona 08028, Spain
[3] Univ Zaragoza, Dept Matemat, C Pedro Cerbuna 12, Zaragoza 50009, Spain
[4] Univ Jaume 1, Dept Matemat, Castellon De La Plana 12071, Spain
[5] Univ Jaume 1, Inst Univ Matemat & Aplicac Castello, Castellon De La Plana 12071, Spain
关键词
R-modules; Gamma-semimodules; Curve singularities; Moduli; Value sets; BRANCHES;
D O I
10.1007/s10801-025-01382-x
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we characterize the value set Delta of the R-modules of the form R+zR for the local ring R associated to a germ xi of an irreducible plane curve singularity with one Puiseux pair. In the particular case of the module of Kahler differentials attached to xi, we recover some results of Delorme. From our characterization of Delta 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.
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页数:20
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