Dual complementar de Newton

• Ano de defesa: 2019
• Autor(a) principal: Santos, Rodrigo Santana dos
• Orientador(a): Dória, André Vinicius Santos
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Programa de Pós-Graduação: Pós-Graduação em Matemática
• Palavras-chave em Português: Matemática; Álgebra; Geometria algébrica; Aplicações racionais; Álgebra de Rees; Dualidade de Newton; Aplicações de Jonquières
• Palavras-chave em Inglês: Rational applications; Algebra of Rees; Newton's duality; Jonquières applications
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://ri.ufs.br/jspui/handle/riufs/11087

In this work we will study Newton complementary dual, a theory originated in the work of A. Simis and B. Costa, later simplified and improved in the work of A. Doria. In a first moment, we will give preliminary notions of Algebraic Geometry, Rational Applications and Rees Algebra, however, under the algebraic view. In the sequence we will discuss the main theme of the dissertation: the duality of Newton and its properties, which were developed having implicit a very important hypothesis, the canonical restrictions. Finally, we will establish some relations between the ideal of presentation of a rational application and its dual via a function, which is not a ring homomorphism, but we will also see that the dual applications of Jonquières are still applications of this type.