| Autor(es): |
Bode, Benjamin
;
Quiceno, Eder L. Sanchez
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | KODAI MATHEMATICAL JOURNAL; v. 48, n. 3, p. 47-pg., 2025-10-01. |
| Resumo | |
Mixed polynomials f : C-2 -> C are polynomials in complex variables u and v as well as their complex conjugates u and v. They are therefore identical to the set of real polynomial maps from R4 to R2. We generalize Mondal's notion of partial non-degeneracy from holomorphic polynomials to mixed polynomials, introducing the concepts of partially non-degenerate and strongly partially non-degenerate mixed functions. We prove that partial non-degeneracy implies the existence of a weakly isolated singularity, while strong partial non-degeneracy implies an isolated singularity. We also compare (strong) partial non-degeneracy with other types of non-degeneracy of mixed functions, such as (strong) inner non-degeneracy, and find that, in contrast to the holomorphic setting, the different properties are not equivalent for mixed polynomials. We then define classes of mixed polynomials for which strong partial non-degeneracy is equivalent to the existence of an isolated singularity. Furthermore, we prove that mixed polynomials that are strongly inner non-degenerate satisfy the strong Milnor condition, resulting in an explicit Milnor (sphere) fibration. (AU) | |
| Processo FAPESP: | 17/25902-8 - Classificação de singularidades reais e complexas |
| Beneficiário: | Eder Leandro Sanchez Quiceno |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |
| Processo FAPESP: | 19/11415-3 - Classificação de Singularidades Reais e Complexas |
| Beneficiário: | Eder Leandro Sanchez Quiceno |
| Modalidade de apoio: | Bolsas no Exterior - Estágio de Pesquisa - Doutorado |