The Noether–Lefschetz theorem

Abstract: The classical Noether–Lefschetz theorem says that for a very general surface $S$ of degree $ \geq 4$ in $\mathbf{P}^3$ over the complex numbers, the restriction map from the divisor class group on $\mathbf{P}^3$ 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).

algebraic geometry

Audience: researchers in the topic

Stanford algebraic geometry seminar

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More seminar information (including slides and videos, when available): agstanford.com