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Hyperbolicity related problems for complete intersection varieties

Part of: (Co)homology theory Special varieties

Published online by Cambridge University Press:  18 November 2013

Damian Brotbek
Damian Brotbek*
Affiliation:
Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France email brotbek@math.unistra.fr
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Abstract

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In this paper we examine different problems regarding complete intersection varieties of high multidegree in a smooth complex projective variety. First we prove an existence theorem for jet differential equations that generalizes a theorem of Diverio. Then we show how one can deduce hyperbolicity for generic complete intersections of high multidegree and high codimension from the known results on hypersurfaces. Finally, motivated by a conjecture of Debarre, we focus on the positivity of the cotangent bundle of complete intersections, and prove some results towards this conjecture; among other things, we prove that a generic complete intersection surface of high multidegree in a projective space of dimension at least four has an ample cotangent bundle.

Keywords

complete intersectionsample cotangent bundlejet differential equations

MSC classification

Secondary: 14M10: Complete intersections 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 3 , March 2014 , pp. 369 - 395
Copyright
© The Author(s) 2013 

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