On the Milnor fibres of initial forms of topologically equivalent holomorphic functions
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909547447189504 |
|---|---|
| author | Sampaio, José Edson |
| author_facet | Sampaio, José Edson |
| contents | Budur, Fernandes de Bobadilla, Le and Nguyen (2022) conjectured that if two germs of holomorphic functions are topologically equivalent, then the Milnor fibres of their initial forms are homotopy equivalent. In this note, we give affirmative answers to this conjecture in the case of plane curves. We show also that a positive answer to this conjecture implies in a positive answer to the famous Zariski multiplicity conjecture both in the case of right equivalence or in the case of hypersurfaces with isolated singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Milnor fibres of initial forms of topologically equivalent holomorphic functions Sampaio, José Edson Algebraic Geometry Complex Variables 14B05, 32S50 Budur, Fernandes de Bobadilla, Le and Nguyen (2022) conjectured that if two germs of holomorphic functions are topologically equivalent, then the Milnor fibres of their initial forms are homotopy equivalent. In this note, we give affirmative answers to this conjecture in the case of plane curves. We show also that a positive answer to this conjecture implies in a positive answer to the famous Zariski multiplicity conjecture both in the case of right equivalence or in the case of hypersurfaces with isolated singularities. |
| title | On the Milnor fibres of initial forms of topologically equivalent holomorphic functions |
| topic | Algebraic Geometry Complex Variables 14B05, 32S50 |
| url | https://arxiv.org/abs/2503.17127 |