Families of hypersurfaces of large degree

Mourougane, Christophe. "Families of hypersurfaces of large degree." Journal of the European Mathematical Society 014.3 (2012): 911-936. <http://eudml.org/doc/277584>.

@article{Mourougane2012,
abstract = {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.},
author = {Mourougane, Christophe},
journal = {Journal of the European Mathematical Society},
keywords = {families of varieties of general type; Lang's problems; jet bundles; Lang’s conjecture; function fields; hypersurfaces; algebraic Morse inequalities; jet spaces; Lang's conjecture; function fields; hypersurfaces; algebraic Morse inequalities; jet spaces},
language = {eng},
number = {3},
pages = {911-936},
publisher = {European Mathematical Society Publishing House},
title = {Families of hypersurfaces of large degree},
url = {http://eudml.org/doc/277584},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Mourougane, Christophe
TI - Families of hypersurfaces of large degree
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 3
SP - 911
EP - 936
AB - 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.
LA - eng
KW - families of varieties of general type; Lang's problems; jet bundles; Lang’s conjecture; function fields; hypersurfaces; algebraic Morse inequalities; jet spaces; Lang's conjecture; function fields; hypersurfaces; algebraic Morse inequalities; jet spaces
UR - http://eudml.org/doc/277584
ER -