Saito bases and standard bases for plane curves

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Felipe Cano
Universidad de Valladolid. Departamento de Álgebra, Análisis Matemático, Geometría y Topología
https://orcid.org/0000-0002-5873-1805
Nuria Corral
Universidad de Cantabria. Departamento de Matem´aticas, Estad´ıstica y Computaci´on
https://orcid.org/0000-0003-3183-8386
David Senovilla-Sanz
Universidad de Cantabria. Departamento de Matem´aticas, Estad´ıstica y Computaci´on
https://orcid.org/0000-0002-8191-8686

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.

Paraules clau
Saito basis, analytic invariants, equisingularity, semimodule, cusp, standard basis, differential values

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Cano, Felipe et al. «Saito bases and standard bases for plane curves». Publicacions Matemàtiques, 2026, vol.VOL 70, núm. 1, p. 203-46, doi:10.5565/PUBLMAT7012608.
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(c) 2026

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