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oai:recercat.cat:2117/4461912026-02-11T04:34:54Zcom_2072_1033col_2072_452950

Curve singularities with one Puiseux pair and value sets of modules over their local rings Alberich Carramiñana, Maria Almirón Cuadros, Patricio Moyano Fernández, Julio José Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica R-modules G-semimodules Curve singularities Moduli Value sets Classificació AMS::14 Algebraic geometry::14H Curves Classificació AMS::13 Commutative rings and algebras::13C Theory of modules and ideals Classificació AMS::13 Commutative rings and algebras::13N Differential algebra Classificació AMS::20 Group theory and generalizations::20N Other generalizations of groups In this paper we characterize the value set of the R-modules of the form R+zRfor 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 ¿,werecoversomeresultsofDelorme.Fromourcharacterizationof weintroduce 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. The first named author is partially supported by PID2019-103849GB-I00 and PID2023-146936NB-I00 financed by the Spanish State Agency MCIN/AEI/10.13039/501100011033/FEDER/UE and 2021SGR-00603 financed by the Generalitat de Catalunya. The second named author is supported by Grant RYC2021-034300-I funded by MICIU/AEI/10.13039/501100011033 and by European Union NextGenerationEU/PRTR and during the elaboration of this work was also supported by the IMAG-Maria de Maeztu grant CEX2020-001105-M / AEI /10.13039/501100011033 and by Spanish Ministerio de Ciencia, Innovación y Universidades PID2020-114750GB-C32/AEI/10.13039/501100011033. The third named author is partially funded by MCIN/AEI/10.13039/501100011033, by "ERDF A way of making Europe" (grant PID2022-138906NB-C22) and by Universitat Jaume I, grants UJI-B2021-02 and GACUJIMA/2024/03. Peer Reviewed Postprint (published version) 2025-03-01 Article Alberich, M.; Almirón, P.; Moyano, J. Curve singularities with one Puiseux pair and value sets of modules over their local rings. «Journal of algebraic combinatorics», 1 Març 2025, vol. 61, núm. 2, article 20. 0925-9899 https://hdl.handle.net/2117/446191 10.1007/s10801-025-01382-x eng https://link.springer.com/article/10.1007/s10801-025-01382-x info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-103849GB-I00/ES/GEOMETRIA, ALGEBRA, TOPOLOGIA Y APLICACIONES MULTIDISCIPLINARES/ info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2023-146936NB-I00/ES/INTERACCIONES DE GEOMETRIA CON ALGEBRA Y APLICACIONES/ info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-114750GB-C32/ES/SINGULARIDADES EN ALGEBRA, GEOMETRIA, TOPOLOGIA, CRIPTOGRAFIA Y SUS APLICACIONES/ info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-138906NB-C22/ES/SISTEMAS LINEALES Y POSITIVIDAD. FOLIACIONES. CODIGOS CUANTICOS Y LOCALMENTE RECUPERABLES/ Open Access 20 p. application/pdf