Restriction of sections of abelian schemes

2003/10/25 by Najmuddin Fakhruddin, Fakhruddin, Najmuddin
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.math/0310405

arxiv created 2003/10/25 · openalex publication_date 2003/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the following result: Let B be a smooth, irreducible, quasi-projective variety over the complex numbers and assume that B has a projective compactification B such that B - B is of codimension at least two in B. Then there exists a family of smooth ireducible curves C_{qq ∈ Q} in B parametrised by an irreducible variety Q such that if p: A → B is an abelian scheme and q ∈ Q is a generic point, then the restriction map on sections A(B) → A(C_q) is an isomorphism. This answers, in a special case, a question of Graber, Harris, Mazur and Starr.

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