As an answer to Mordell problem over function fields, Grauert and Manin showed that a non-isotrivial algebraic family of compact complex hyperbolic curves has finitely many
sections. We consider a generic moving enough family of high enough degree hypersurfaces
in a complex projective space. We show the existence of a strict closed subset of its total
space that contains the image of all its sections.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/5285