Computing a Saito basis from a standard basis

Abstract

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 compute 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.