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 $Y\in |L|$ 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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Additional Information
G. V. Ravindra
Affiliation:
Department of Mathematics, Washington University, St. Louis, Missouri 63130
MR Author ID:
705313
Email:
ravindra@math.wustl.edu
V. Srinivas
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005, India
MR Author ID:
194380
Email:
srinivas@math.tifr.res.in
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
