Chennai Mathematical Institute


3.30 p.m.
Sections of families of hypersurfaces of large degree

Christophe Mourougane
University of Rennes, France.


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.