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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

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

Lira, Dayane Santos de 24 February 2017 (has links)
Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-22T13:57:08Z No. of bitstreams: 1 arquivototal.pdf: 1762696 bytes, checksum: 53bf47b7590ebc1271d2f0d81822f00c (MD5) / Made available in DSpace on 2017-08-22T13:57:08Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1762696 bytes, checksum: 53bf47b7590ebc1271d2f0d81822f00c (MD5) Previous issue date: 2017-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / 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. / Este trabalho objetiva determinar a quantidade máxima de retas duas a duas disjuntas que uma superfície não singular de grau d em P3 pode conter. No caso dos graus d = 1 e d = 2 verificamos que estes valores s~ao zero e in nito, respectivamente. Al em disso, no caso de grau d = 3 mostramos que o n umero m aximo de retas duas a duas disjuntas e 6, ditas con gura c~oes foram estudadas em 1863 pelo sui co Ludwig Schl a i (1814-1895) em [15]. Para o caso d = 4, em 1975 o russo Viacheslav Nikulin em [10] mostrou que as superf cies qu articas n~ao singulares cont^em no m aximo 16 retas duas a duas disjuntas. No nosso trabalho, conseguimos mostrar que a famosa qu artica de Schur atinge essa cota e que qu artica de Fermat possui no m aximo 12 retas duas a duas disjuntas. Determinamos ainda cotas inferiores para o n umero m aximo de retas duas a duas disjuntas no caso de superf cies n~ao singulares de grau d 5. Por exemplo, a fam lia de Rams em [11] nos permite achar uma dessas cotas inferiores.

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