Saito bases and standard bases for plane curves

In this paper we describe how to compute a Saito basis of a cusp, a plane curve with only one Puiseux pair. Moreover, the 1-forms of the Saito basis that we obtain are characterized in terms of their divisorial orders associated to the "cuspidal" divisor of the minimal reduction of singula...

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Detalles Bibliográficos
Autores: Cano, Felipe|||0000-0002-5873-1805, Corral, Nuria|||0000-0003-3183-8386, Senovilla-Sanz, David|||0000-0002-8191-8686
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:324083
Acceso en línea:https://ddd.uab.cat/record/324083
https://dx.doi.org/urn:doi:10.5565/PUBLMAT7012608
Access Level:acceso abierto
Palabra clave:Saito basis
Analytic invariants
Equisingularity
Semimodule
Cusp
Standard basis
Differential values
Descripción
Sumario:In this paper we describe how to compute a Saito basis of a cusp, a plane curve with only one Puiseux pair. Moreover, the 1-forms of the Saito basis that we obtain are characterized in terms of their divisorial orders associated to the "cuspidal" divisor of the minimal reduction of singularities of the cusp. We also introduce a new family of analytic invariants for plane curves computed in terms of Saito bases.