A characterization of quasi-homogeneity in terms of liftable vector fields
Algebraic Geometry
2025-04-09 v1 Dynamical Systems
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 multipliticy 3, then it admits a substantial unfolding if and only if it is quasi-homogeneous. Based on this we pose the following conjecture: a finitely determined map-germ is quasi-homogeneous if and only if it admits a substantial unfolding.
Cite
@article{arxiv.2504.06062,
title = {A characterization of quasi-homogeneity in terms of liftable vector fields},
author = {Ignacio Breva Ribes and Raúl Oset Sinha},
journal= {arXiv preprint arXiv:2504.06062},
year = {2025}
}