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Sections of families of hypersurfaces of large degree

Posted in
Christophe Mourougane
Thu, 2011-12-01 10:30 - 12:00
MPIM Lecture Hall

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.

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