The Grothendieck-Lefschetz Theorem for Normal Projective Varieties

Ravindra Girivaru; Vasudevan Srinivas

The Grothendieck-Lefschetz Theorem for Normal Projective Varieties

University of Missouri-St. Louis

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

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	American English
Journal	Journal of Algebraic Geometry
State	Published - Oct 25 2005

Disciplines

Mathematics

Cite this

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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.",

author = "Ravindra Girivaru and Vasudevan Srinivas",

year = "2005",

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language = "American English",

journal = "Journal of Algebraic Geometry",

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T1 - The Grothendieck-Lefschetz Theorem for Normal Projective Varieties

AU - Girivaru, Ravindra

AU - Srinivas, Vasudevan

PY - 2005/10/25

Y1 - 2005/10/25

N2 - 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.

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 - http://www.cs.umsl.edu/~girivaru/gl.pdf

M3 - Article

JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

ER -

The Grothendieck-Lefschetz Theorem for Normal Projective Varieties

Abstract

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