The grothendieck-lefschetz theorem for normal projective varieties

G. V. Ravindra; V. Srinivas

doi:10.1090/S1056-3911-05-00421-2

The grothendieck-lefschetz theorem for normal projective varieties

G. V. Ravindra
, V. Srinivas

Mathematics

Washington University St. Louis

Research output: Contribution to journal › Article › peer-review

47 Scopus citations

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 Cl(X) → Cl(Y) is an isomorphism for a general member Y ∈ |L| provided that dim X ≥ 4. This is a generalization of the Grothendieck- Lefschetz theorem, for divisor class groups of singular varieties.

Original language	English
Pages (from-to)	563-590
Number of pages	28
Journal	Journal of Algebraic Geometry
Volume	15
Issue number	3
DOIs	https://doi.org/10.1090/S1056-3911-05-00421-2
State	Published - Jul 2006

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title = "The grothendieck-lefschetz theorem for normal projective varieties",

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 Cl(X) → Cl(Y) is an isomorphism for a general member Y ∈ |L| provided that dim X ≥ 4. This is a generalization of the Grothendieck- Lefschetz theorem, for divisor class groups of singular varieties.",

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AB - 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) → Cl(Y) is an isomorphism for a general member Y ∈ |L| provided that dim X ≥ 4. This is a generalization of the Grothendieck- Lefschetz theorem, for divisor class groups of singular varieties.

UR - https://www.scopus.com/pages/publications/33745303041

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DO - 10.1090/S1056-3911-05-00421-2

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VL - 15

SP - 563

EP - 590

JO - Journal of Algebraic Geometry

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IS - 3

ER -

The grothendieck-lefschetz theorem for normal projective varieties

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