Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

The Grothendieck-Lefschetz theorem for normal projective varieties


Authors: G. V. Ravindra and V. Srinivas
Journal: J. Algebraic Geom. 15 (2006), 563-590
DOI: https://doi.org/10.1090/S1056-3911-05-00421-2
Published electronically: October 25, 2005
MathSciNet review: 2219849
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Abstract | References | Additional Information

Abstract: 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 $ \operatorname{Cl} (X)\to \operatorname{Cl}(Y)$ is an isomorphism for a general member $ Y\in \vert L\vert$ 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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Additional Information

G. V. Ravindra
Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130
Email: ravindra@math.wustl.edu

V. Srinivas
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005, India
Email: srinivas@math.tifr.res.in

DOI: https://doi.org/10.1090/S1056-3911-05-00421-2
Received by editor(s): April 21, 2005
Received by editor(s) in revised form: May 31, 2005, and June 15, 2005
Published electronically: October 25, 2005
Additional Notes: Srinivas was partially supported by a Swarnajayanthi Fellowship of the D.S.T

American Mathematical Society