3.30 p.m.
Sections of families of hypersurfaces of large degree
Christophe Mourougane
University of Rennes, France.
20-03-12

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Abstract

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.