The Grothendieck-Lefschetz theorem for normal projective varieties

Details The Grothendieck-Lefschetz theorem for normal projective varieties The Grothendieck-Lefschetz theorem for normal projective varieties

2005-11-05

arxiv.org/abs/math/0511134v1

Mathematics

Algebraic Geometry

21 pages, no figures, to appear in J. Algebraic Geometry

Scientific paper

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 $\Cl(X)\to \Cl(Y)$ is an isomorphism for a general member $Y\in
|L|$ provided that $\dim{X}\geq 4$. This is a generalization of the
Grothendieck-Lefschetz Theorem, for divisor class groups of singular varieties.

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