A remark on two notions of order of contact

TL;DR

This paper compares two different ways of measuring how closely an ideal in holomorphic function germs approaches contact, providing examples where these measures do not agree.

Contribution

It highlights differences between two notions of order of contact and offers explicit examples illustrating their divergence.

Findings

The two measures of contact can differ significantly.

Explicit examples demonstrate the divergence between the notions.

The paper clarifies the relationship between these two contact measurements.

Abstract

We recall two measurements of the order of contact of an ideal in the ring of germs of holomorphic functions at a point and we provide a class of examples in which they differ.