On the Saito basis for plane curves

TL;DR

This paper investigates the Saito module and torsion submodule of analytic plane curves, providing an algorithm to compute these invariants and applying it to curves with low multiplicity.

Contribution

It introduces a new method for computing the Saito module and torsion submodule, enabling analysis of plane curves with multiplicity up to three.

Findings

Computed invariants for low-multiplicity plane curves

Developed an algorithm for Saito module calculation

Enhanced understanding of analytic invariants in plane curves

Abstract

We present some results concerning the Saito module and the torsion submodule of an analytic plane curve, and we provide a method for computing them. Using this algorithm, we compute analytic invariants for plane curves with multiplicity less than or equal to three.