Work

A characterization of quasi-homogeneity in terms of liftable vector fields

Year: 2026

Type: article

Abstract: We prove under certain conditions that any stable unfolding of a quasi-homogeneous map-germ with finite singularity type is substantial. We then prove that if an equidimensional map-germ is finitely determined, of corank 1, and either it admits a minimal stable unfolding or it is of multiplicity 3, then it admits a substantial unfolding if and only if it is quasi-homogeneous in some coordinate system. Based on this, we pose the following conjecture: a finitely determined map-germ is quasi-homogeneous in some coordinate system if and only if it admits a substantial unfolding.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2026.10131

Authors: Ignacio Breva Ribes, Raúl Oset Sinha

Institution: Universitat de València

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Universitat de València, European Regional Development Fund, Agencia Estatal de Investigación