Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-16T14:45:10Z No. of bitstreams: 1 arquivototal.pdf: 923276 bytes, checksum: 684d210a074aefcedef691723f8d04e0 (MD5) / Made available in DSpace on 2017-08-16T14:45:10Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 923276 bytes, checksum: 684d210a074aefcedef691723f8d04e0 (MD5) Previous issue date: 2016-03-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / It is well-known that planes and quadric surfaces in the projective space contain in - nitely many lines. For smooth cubic surface Cayley and Salmon, 1847, (and Clebsch later) proved that it has exactly 27 lines. For degree 4, in 1943 Segre proved that the maximum number of lines contained in a smooth quartic surface is 64. For surfaces of degree greater than 4 this number is unknown. In this work, we are going to explore what is the maximum number of lines that a smooth complex surface of degree d of the family Fd ; may contain. Thus, we obtain a lower bound to the maximum number of lines that non singular surfaces of degree d in P3 may contain. We emphasize that the determination of this numbers is based on the Klein's classi cation theorem of nitte subgroups of Aut(P1) and the study of 􀀀C; the subgroup of Aut(P1) whose elements leaves invariant the nite subset C of P1: / Sabe-se que planos e superf cies qu adricas no espa co projetivo cont em in nitas retas. No caso de uma superf cie c ubica n~ao singular Cayley e Salmon, em 1847, (e Clebsch, mais tarde) provaram que ela cont em exatamente 27 retas. No caso de grau 4, em 1943 Segre provou que o n umero m aximo de retas contidas numa superf cie qu artica n~ao singular e 64. Para superf cies de grau maior que 4 esse n umero e desconhecido. Neste trabalho vamos explorar qual e a quantidade m axima de retas que uma superf cie complexa n~ao singular de grau d na fam lia Fd ; pode conter. Assim obtemos uma cota inferior para o n umero m aximo de retas que as superf cies n~ao singulares de grau d em P3 podem conter. Salientamos que a determina c~ao destes n umeros tem como base o Teorema de Classi ca cao de Klein dos sugbrupos nitos de Aut(P1) e o estudo dos subgrupos 􀀀C de Aut(P1) que deixam invariante um subconjunto nito C de P1: