Liftable vector fields over corank one multigerms

TL;DR

This paper introduces a systematic method for constructing liftable vector fields over certain analytic multigerms with corank at most one, focusing on those admitting a one-parameter stable unfolding, advancing the understanding of their geometric structure.

Contribution

It provides a new systematic approach to construct all liftable vector fields over corank one multigerms with stable unfoldings, filling a gap in singularity theory.

Findings

Constructed all liftable vector fields for specified multigerms.

Established a systematic method applicable to corank at most one cases.

Enhanced understanding of the structure of liftable vector fields in singularity theory.

Abstract

In this paper, a systematic method is given to construct all liftable vector fields over an analytic multigerm $f: (\mathbb{K}^n, S)\to (\mathbb{K}^p,0)$ of corank at most one admitting a one-parameter stable unfolding.