A characterization of quasi-homogeneity in terms of liftable vector fields
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916679173275648 |
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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 |