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Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2023.tde-12092023-183245
Document
Author
Full name
Eder Leandro Sanchez Quiceno
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2023
Supervisor
Committee
Santos, Raimundo Nonato Araújo dos (President)
Ballesteros, Juan José Nuño
Libardi, Alice Kimie Miwa
Ruas, Maria Aparecida Soares
Title in Portuguese
Enlaçamentos de singularidades mistas
Keywords in Portuguese
Enlaçamento algébrico real
Enlaçamento da singularidade
Enlaçamentos fibrados
Poliedro de Newton
Polinômios semiholomorfos
Singularidades de polinômios mistos
Abstract in Portuguese
Neste trabalho apresentamos métodos para estudar enlaçamentos e singularidades de polinômios mistos a partir de novas condições de não-degeneração chamadas de não-degeneração interior (NDI), não-degeneração parcial (NDP), não-degeneração interior forte (FNDI) e não-degeneração parcial forte (FNDP). Além disso mostramos que em certas famílias de polinômios mistos a estrutura topológica do enlaçamento é completamente determinada nas faces compactas do bordo de Newton. Além do mais, utilizamos a condição FNDI para fornecer famílias de realizações de enlaçamentos algébricos reais que nos permite explorar a conexão entre a conjectura de Benedetti-Shiota e singularidades mistas.
Title in English
Links of mixed singularities
Keywords in English
Fibered links
Link of singularity
Newton polyedron
Real algebraic link
Semiholomorphic polynomials
Singularities of mixed polynomials
Abstract in English
In this work we introduce methods to study links and singularities of mixed polynomials through new conditions of non-degeneracies called inner non-degeneracy (IND), partial nondegeneracy (PND), strong inner non-degeneracy (SIND) and strong partial non-degeneracy (SPND). Moreover, we show that for certain families of mixed polynomials, the topological structure of the link is completely described on the compact faces of the Newton boundary. Furthermore, we use the SIND condition to provide families of realizations of real algebraic links that allow us to explore the connexion between the Benedetti-Shiota conjecture and the mixed singularities.
 
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Publishing Date
2023-09-12
 
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