Families of hypersurfaces of large degree

  • Christophe Mourougane

    Institut de Recherche Mathématiques de Rennes (IRMAR), France


Grauert and Manin showed that a non-isotrivial 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.

Cite this article

Christophe Mourougane, Families of hypersurfaces of large degree. J. Eur. Math. Soc. 14 (2012), no. 3, pp. 911–936

DOI 10.4171/JEMS/322