Singularities of Frontal Surfaces

TL;DR

This paper classifies singularities of frontal surfaces of corank one, introduces frontalisation for fold singularities, and explores conditions for finite codimension, including curves and conjectures related to these surfaces.

Contribution

It introduces the notion of frontalisation for fold singularities and characterizes finite codimension conditions via reduced curves.

Findings

Frontal surfaces of corank one have finite codimension iff certain curves are reduced.

Introduces frontalisation for fold-type singularities.

Discusses frontal versions of Marar-Mond formulas and Mond's conjecture.

Abstract

We consider singularities of frontal surfaces of corank one and finite frontal codimension. We look at the classification under left-right-equivalence and introduce the notion of frontalisation for singularities of fold type. We define the cuspidal and the transverse double point curves and prove that the frontal has finite codimension if and only if both curves are reduced. Finally, we also discuss about the frontal versions of the Marar-Mond formulas and the Mond's conjecture.