https://repositorio.ufpb.br/jspui/handle/tede/6873 PPGMAT Sat, 06 Jun 2026 13:48:29 GMT 2026-06-06T13:48:29Z https://repositorio.ufpb.br/jspui/handle/123456789/38051 Título: Limites de curvas planas duais via séries de Puiseux Autor(es): Custódio, Rony Héron Silva Orientador: Sousa, Wállace Mangueira de Abstract: This work addresses the limit of plane dual curves, a topic in algebraic geome- try that seeks to understand what happens to curves when they undergo degeneracy processes. In such situations, the dual of the limiting curve does not always coincide with the limit of the duals, and therefore a more careful examination is required. First, we introduce some fundamental concepts, such as Puiseux series, discri- minants of univariate polynomials, and intersections in the projective plane. Next, we address the duality between points and lines in this setting and apply this concept to the study of the dual curve of a smooth projective plane curve. We then examine how this duality behaves within flat families of curves. The main result provides a precise formula for describing the limit of such dual curves, relating its components to the duals of each component of the special fiber of the family, as well as to certain discriminants. Finally, examples illustrate the theorem and demonstrate the practical utility of the theory developed. The research thus seeks to bring the reader closer to a more intuitive understanding of how curves and their duals interact in limiting situations. Editor: Universidade Federal da Paraíba Tipo: Dissertação Fri, 31 Oct 2025 00:00:00 GMT https://repositorio.ufpb.br/jspui/handle/123456789/38051 2025-10-31T00:00:00Z https://repositorio.ufpb.br/jspui/handle/123456789/37773 Título: Sobre uma desigualdade do tipo Hardy-Sobolev e aplicações Autor(es): Lima, Francisco Jonatã Chaves de Orientador: Medeiros, Everaldo Souto de Abstract: In this work, we present a Hardy-Sobolev type inequality in cylindrical domains and, as a consequence, derive some Sobolev embeddings into weighted Lebesgue spaces. We prove that the attainability of the best constant for these weighted embeddings is equivalent to establishing the existence of ground state solutions for a class of elliptic problems in R. Regularity and behavior of the minimizers are also analyzed. As an application of the obtained embeddings, we prove existence and non-existence results for a class of elliptic problems with critical growth. Editor: Universidade Federal da Paraíba Tipo: Dissertação Wed, 19 Feb 2025 00:00:00 GMT https://repositorio.ufpb.br/jspui/handle/123456789/37773 2025-02-19T00:00:00Z https://repositorio.ufpb.br/jspui/handle/123456789/37772 Título: Uma introdução às variedades tóricas Autor(es): Lima, Fagner da Silva Orientador: Pereira, Miriam da Silva Abstract: In this work, we studied about affine toric varieties related to polyhedral lattice cones that are strongly convexes. From the collage of these varieties, we defined the toric variety, as well as describing some of their properties. Besides, we analyzed the action of the algebraic torus in the toric varieties in order to describe their orbits. Editor: Universidade Federal da Paraíba Tipo: Dissertação Tue, 20 Mar 2018 00:00:00 GMT https://repositorio.ufpb.br/jspui/handle/123456789/37772 2018-03-20T00:00:00Z https://repositorio.ufpb.br/jspui/handle/123456789/37655 Título: Estimativas de Schauder Autor(es): Silva, Robson Lucas Soares da Orientador: Araújo, Damião Júnio Gonçalves Abstract: In this work, we study regularity of solutions of second order PDE’s. More precisely, we study universal C 2,α regularity estimates of solutions, which are also known as Schauder estimates. We divide the thesis in three parts: in the first part, we study results of C 2,α solutions of Poisson Equations which are a-priori α-H ̈older continuous. In the second part, we study C 2,α regularity of solutions of linear second order elliptic PDE’s, with C α coefficients, through an interior estimate. Finally, we study the C 2,α regularity of viscosity solutions of fully non-linear second order elliptic PDE’s. Editor: Universidade Federal da Paraíba Tipo: Dissertação Fri, 24 Jul 2020 00:00:00 GMT https://repositorio.ufpb.br/jspui/handle/123456789/37655 2020-07-24T00:00:00Z