On the moduli space of quasi-homogeneous functions
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2020
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917761816461312 |
|---|---|
| author | Câmara, Leonardo Meireles Ruas, Maria Aparecida Soares |
| author_facet | Câmara, Leonardo Meireles Ruas, Maria Aparecida Soares |
| contents | We relate the moduli space of analytic equivalent germs of reduced quasi-homogeneous functions at $(\mathbb{C}^2,0)$ with their bi-Lipschitz equivalence classes. We show that any non-degenerate continuous family of (reduced) quasi-homogeneous functions with constant Henry-Parusiński invariant is analytically trivial. Further we show that there are only a finite number of distinct bi-Lipschitz classes among quasi-homogeneous functions with the same Henry-Parusiński invariant providing a maximum quota for this number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_03778 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the moduli space of quasi-homogeneous functions Câmara, Leonardo Meireles Ruas, Maria Aparecida Soares Complex Variables 32S05 (Primary) 14J17 (Secondary) We relate the moduli space of analytic equivalent germs of reduced quasi-homogeneous functions at $(\mathbb{C}^2,0)$ with their bi-Lipschitz equivalence classes. We show that any non-degenerate continuous family of (reduced) quasi-homogeneous functions with constant Henry-Parusiński invariant is analytically trivial. Further we show that there are only a finite number of distinct bi-Lipschitz classes among quasi-homogeneous functions with the same Henry-Parusiński invariant providing a maximum quota for this number. |
| title | On the moduli space of quasi-homogeneous functions |
| topic | Complex Variables 32S05 (Primary) 14J17 (Secondary) |
| url | https://arxiv.org/abs/2004.03778 |