The Grothendieck-Lefschetz theorem for normal projective varieties

الأصل · EN

We prove that for a normal projective variety X in characteristic 0, and a base-point free ample line bundle L on it, the restriction map of divisor class groups (X)→ (Y) is an isomorphism for a general member Y∈ |L| provided that X≥ 4. This is a generalization of the Grothendieck-Lefschetz Theorem, for divisor class groups of singular varieties.