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

( slides )

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

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Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

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