Relating Catlin and D'Angelo $q$-types

TL;DR

This paper clarifies the relationship between Catlin and D'Angelo q-types, showing that Catlin's type equals the generic normalized order of contact along curves, linking two key measures of complex variety contact with real hypersurfaces.

Contribution

It establishes that Catlin's q-type equals the generic normalized order of contact along curves, connecting two fundamental contact measurements.

Findings

Catlin q-type equals the generic normalized order of contact.

The relationship clarifies the measurement of contact of complex varieties.

Provides a unified understanding of q-type measurements.

Abstract

We clarify the relationship between the two most standard measurements of the order of contact of q-dimensional complex varieties with a real hypersurface, the Catlin and D'Angelo $q$-types, by showing that the former equals the generic value of the normalized order of contact measured along curves whose infimum is by definition the D'Angelo $q$-type.