EXAMPLES OF MILNOR AND MILNOR-LÊ FIBRATIONS FOR A FAMILY OF MIXED POLYNOMIALS

Rafaella de Souza Martins; Nivaldo de Góes Grulha Júnior

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Trabalho

Título do Trabalho

EXAMPLES OF MILNOR AND MILNOR-LÊ FIBRATIONS FOR A FAMILY OF MIXED POLYNOMIALS

Autores

Rafaella de Souza Martins
Nivaldo de Góes Grulha Júnior

Modalidade

Resumo simples

Área temática

CEXA - Ciências Exatas e da Terra

Data de Publicação

04/08/2025

País da Publicação

Brasil

Idioma da Publicação

Português

Página do Trabalho

https://www.even3.com.br/anais/congresso-brasileiro-interdisciplinar-ciencia-tecnologia/1211563-examples-of-milnor-and-milnor-le-fibrations-for-a-family-of-mixed-polynomials

ISSN

2764-0582

Palavras-Chave

Milnor fibration; Milnor-Lê fibration; non-isolated critical value; mixed polynomials.

Resumo

In 2002’s authors Ruas, Seade and Verjovsky started with the study of the existence of Milnor and Milnor-Lê fibrations of the following real analytic functions ψ_(F,X) (z)=∑_(j=1)^n〖k_j ¯(t_j )〗 z_(σ_j)^(a_j ), (1) where k_j,t_j∈C^*, a_j,b_j∈Z^+,j=1,⋯,n and {σ_1,⋯,σ_n} is a permutation of the set {1,⋯,n}. When this family of mixed weighted homogeneous polynomials has isolated singularity, by Milnor, we can assume the existence of Milnor and Milnor-Lê fibrations. We work with a class of real analytical functions with non-isolated critical value, these are of the form the (1), with a_j = b_j for at least one j and a_j≠ b_j for at least one j. This functions does not satisfy the conditions of the work of Ruas, Seade and Verjovsky. We conclude the existence of Milnor and Milnor-Lê fibrations, using some results of the authors Cisneros-Molina, Menegon, Seade and Snoussi. We show some characteristics of this family to confirm the existence of the fiber over the regular values and the critical values and the relation between them. Its possible to made the existence of a locally trivial bundle on the discriminant of ψ_(F,X) and compare the bundles for a particular case of this family. The ψ_(F,X) possesses interesting properties, a particular case of which is ICIS and ψ_(F,X)^(-1) (d),d∈Δ_(ψ_(F,X) ) are regular manifold.

Título do Evento: VI Congresso Brasileiro Interdisciplinar em Ciência e Tecnologia
Título dos Anais do Evento: Anais do Congresso Brasileiro Interdisciplinar em Ciência e Tecnologia
Nome da Editora: Even3
Meio de Divulgação: Meio Digital

Como citar

MARTINS, Rafaella de Souza; JÚNIOR, Nivaldo de Góes Grulha. EXAMPLES OF MILNOR AND MILNOR-LÊ FIBRATIONS FOR A FAMILY OF MIXED POLYNOMIALS.. In: Anais do Congresso Brasileiro Interdisciplinar em Ciência e Tecnologia. Anais...Diamantina(MG) Online, 2025. Disponível em: https//www.even3.com.br/anais/congresso-brasileiro-interdisciplinar-ciencia-tecnologia/1211563-EXAMPLES-OF-MILNOR-AND-MILNOR-LE-FIBRATIONS-FOR-A-FAMILY-OF-MIXED-POLYNOMIALS. Acesso em: 10/11/2025