# Families of hypersurfaces of large degree

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 3, page 911-936
- ISSN: 1435-9855

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topMourougane, 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 -

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