# The Noether--Lefschetz theorem

@inproceedings{Ji2021TheNT, title={The Noether--Lefschetz theorem}, author={Lena Ji}, year={2021} }

We show that if X ⊂ P k is a normal variety of dimension n ≥ 3 and H ⊂ P k a very general hypersurface of degree d = 4 or ≥ 6, then the restriction map Cl(X) → Cl(X ∩H) is an isomorphism up to torsion. If n ≥ 4, the result holds for d ≥ 2.

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