The Noether–Lefschetz theorem

Lena Ji (Princeton/Michigan)

11-Jun-2021, 19:00-20:00 (20 months ago)

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 )

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Stanford algebraic geometry seminar

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