Sobre o número máximo de retas em superfícies de grau d em P3

Abstract

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: