The Noether–Lefschetz theorem

The classical Noether–Lefschetz theorem says that for a very general surface S of degree ≥ 4 in P^3 over the complex numbers, the restriction map from the divisor class group on P^3 to S is an isomorphism. In this talk, we give an elementary proof of Noether–Lefschetz. We do not use any Hodge theory, cohomology, or monodromy. This argument has the additional advantage that it works over fields of arbitrary characteristic and for singular varieties (for Weil divisors).

The synchronous discussion for Lena Ji’s talk is taking place not in zoom-chat, but at https://tinyurl.com/2021-06-11-lj  (and will be deleted after ~3-7 days).