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

Fuente: arXiv
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Main Authors: Ribes, Ignacio Breva, Sinha, Raúl Oset
Format: Preprint
Published: 2025
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author Ribes, Ignacio Breva
Sinha, Raúl Oset
author_facet Ribes, Ignacio Breva
Sinha, Raúl Oset
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_06062
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A characterization of quasi-homogeneity in terms of liftable vector fields
Ribes, Ignacio Breva
Sinha, Raúl Oset
Algebraic Geometry
Dynamical Systems
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.
title A characterization of quasi-homogeneity in terms of liftable vector fields
topic Algebraic Geometry
Dynamical Systems
url https://arxiv.org/abs/2504.06062