2013/04/14 by Morihiko Saito, Saito, Morihiko
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1304.3923
openalex publication_date 2013/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If there is a topologically locally constant family of smooth algebraic varieties together with an admissible normal function on the total space, then the latter is constant on any fiber if this holds on some fiber. Combined with spreading out, it implies for instance that an irreducible component of the zero locus of an admissible normal function is defined over k if it has a k-rational point where k is an algebraically closed subfield of the complex number field with finite transcendence degree. This generalizes a result of F. Charles that was shown in case the normal function is associated with an algebraic cycle defined over k.