1993/11/10 by Atsushi Moriwaki, Moriwaki, Atsushi
Mathematics · Medicine · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Magnolia and Illicium research #Meromorphic and Entire Functions #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9311003
9 pages, AmSTeX
openalex publication_date 1993/11/10 · arxiv created 1993/12/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be a function field of one variable over an algebraically closed field of characteristic zero, X a geometrically irreducible smooth projective variety over F, and L a line bundle on X. In this note, we will prove that if the contangent bundle of X is ample and X is non-isotrivial, then there are a proper closed algebraic set Y of X and a constant A > 0 such that hL(P) <= A d(P) + O(1) for all P ∈ X(F) Y(F), where hL(P) is a geometric height of P with respect to L and d(P) is the geometric logarithmic discriminant of P. As corollary of the above height inequality, we can recover Noguchi's theorem, i.e. there is a non-empty Zariski open set U of X with U(F) = ∅.