A brief survey of Noether-Lefschetz problems
§1 The Noether-Lefschetz Theorem
The starting point was the following claim (M. Noether, 1882) :
Theorem 1.1.1 (Noether-Lefschetz)
If S is a general surface of degree d 4 in P
, then Pic S = Z
generated by 0s(l).
M. Noether did not actually give a proof, but only what we
nowadays call a plausibility argument, based on a parameter
count. Nevertheless it is worth reproducing his ideas here in view
of understanding the global picture and also the meaning of the
word "general" in the theorem.
As well known there are only countably many families of
Received by the editor on February 10, 1989, and, in revised form,
on March 13, 1990.