Hirzebruch surfaces for "n" > 0 have a special rational curve "C" on them: The surface is the projective bundle of "O"(−"n") and the curve "C" is the zero section. This curve has self-intersection number −"n", and is the only irreducible curve with negative self intersection number. The only irreducible curves with zero self intersection number are the fibers of the Hirzebruch surface (considered as a fiber bundle over P1). The Picard group is generated by the curve "C" and one of the fibers, and these generators have intersection matrix