Remarks on S. Lang's conjecture over function fields

Details Remarks on S. Lang's conjecture over function fields Remarks on S. Lang's conjecture over function fields

1994-12-24

arxiv.org/abs/alg-geom/9412021v1

Mathematics

Algebraic Geometry

6 pages, AmSTeX

Scientific paper

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

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