Remarks on S. Lang's conjecture over function fields

摘要

In this short note, we will show the following weak evidence of S. Langconjecture over function fields. Let f : X ---> Y be a projective andsurjective morphism of algebraic varieties over an algebraically closed field kof characteristic zero, whose generic fiber is geometrically irreducible and ofgeneral type. If f is not birationally trivial, then there are countably manyproper closed varieties { Z_i } of X such that every quasi-section of f iscontained in the union of Z_i.