Geodesic
Families of hypersurfaces of large degree
Journal of the European Mathematical Society, Tome 14 (2012) no. 3, pp. 911-936

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DOI

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.
DOI : 10.4171/jems/322
Classification : 14-XX, 32-XX, 00-XX
Keywords: Families of varieties of general type, Lang's problems, jet bundles 
Christophe Mourougane. Families of hypersurfaces of large degree. Journal of the European Mathematical Society, Tome 14 (2012) no. 3, pp. 911-936. doi: 10.4171/jems/322
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     author = {Christophe Mourougane},
     title = {Families of hypersurfaces of large degree},
     journal = {Journal of the European Mathematical Society},
     pages = {911--936},
     year = {2012},
     volume = {14},
     number = {3},
     doi = {10.4171/jems/322},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/322/}
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