Noether–Lefschetz Theorem

Noether–Lefschetz Theorem states that a sufficiently general surface of a 3-dimensional complex projective space has $Z$ as its Picard group. Griffiths and Harris gave a more algebraic proof of this fact than the one proposed by Lefschetz. It uses a construction of a family of surfaces that degenerates to a reducible surface, and a computation of a Picard group of this reducible fiber.