Sobre o número máximo de retas duas a duas disjuntas em superfícies não singulares em P3

• Ano de defesa: 2017
• Autor(a) principal: Lira, Dayane Santos de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Retas Duas a Duas Disjuntas; Superfície de Fermat; Quártica de Schur; Família de Rams; Pairwise Disjoint Lines; Fermat Surface; Schur's Quartic; Rams's Family; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/9294

This work aims to determine the maximum number of pairwise disjoint lines that a non-singular surface of degree d in P3 can contain. In the case of degrees d = 1 and d = 2 we found that these values are zero and in nite, respectively. Furthermore, in the case of degree d = 3 we did show that the maximum number of pairwise disjoint lines is 6, these con gurations were studied in 1863 by the Swiss Ludwig Schl a i (1814-1895) in [15]. For the case d = 4, in 1975 the Russian Viacheslav Nikulin in [10] showed that non-singular quartic surfaces contain at most 16 pairwise disjoint lines. In our work, we have been able to show that Schur's famous quartic achieves this bound and that Fermat's quartic has at most 12 pairwise disjoint lines. We also determined lower bounds for the maximum number of pairwise disjoint lines in the case of non-singular surfaces of degree d 5. For example, the Rams's family in [11] allows us to nd one of these lower bounds.