Links of mixed singularities

Author(s)

Eder Leandro Sanchez Quiceno

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2023-06-27

Examining board members

Raimundo Nonato Araújo dos Santos; Juan José Nuño Ballesteros; Alice Kimie Miwa Libardi; Maria Aparecida Soares Ruas

• Advisor: Raimundo Nonato Araújo dos Santos; Osamu Saeki

Abstract

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. (AU)

• FAPESP's process: 17/25902-8 - Classification of real and complex singularities
• Grantee: Eder Leandro Sanchez Quiceno
• Support Opportunities: Scholarships in Brazil - Doctorate