On deformations of isolated singularities of polar weighted homogeneous mixed polynomials

TL;DR

This paper studies how to deform isolated singularities in a specific class of polar weighted homogeneous mixed polynomials, demonstrating the existence of deformations with only simple, well-understood singularities.

Contribution

It introduces a method to deform isolated singularities of polar weighted homogeneous mixed polynomials to achieve only definite fold and mixed Morse singularities.

Findings

Existence of deformations with only definite fold singularities

Existence of deformations with only mixed Morse singularities

Characterization of singularity types in deformations

Abstract

In the present paper, we deform isolated singularities of a certain class of polar weighted homogeneous mixed polynomials, and show that there exists a deformation which has only definite fold singularities and mixed Morse singularities.