Cálculo das retas numa superfície cúbica em P3

• Ano de defesa: 2011
• Autor(a) principal: Assis Junior, Geraldo de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraí­ba; BR; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Superfície cúbica; Contagem das retas; Espaço projetivo; Surface cubic; Computation of lines; Projective space; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/7466

In this work we study cubic surfaces in P3. More specically, we take care to count the number of lines on these surfaces. In chapter one we proved that the number of lines on a non-singular cubic surface in P3 is 27. In chapter two, as the motivation for chapter three, we focused in the classifcation of singularities of plane curves. For the singular case, discussed in chapter three, we used two algorithm to compute the number of lines. The first one consists in to divide the computation in six packages, which are actually the open set of the grassmannian G(2; 4), and in each open set we count the lines contained on the given surface. The second algorithm consists of dividing the lines on S in two packages: The package of lines passing through P and those lines that not passing through P but they are contained in a plane that contain some line passing through P, here P is an isolated singularity of the given surface.